diff --git a/README.md b/README.md
index 204aad9..bbeca98 100644
--- a/README.md
+++ b/README.md
@@ -12,7 +12,7 @@ Validated:
 - The registration chain ran live against Apple (2026-10-02→04, spec rev 26): Albert activation, the packed APNs courier, the full GSA sign-in (SRP, trusted-device 2FA, PET delivery, postdata), then IDS authenticate and register — both green, `mailto:` handle active. The earlier 409 refusals turned out to be Apple's validation-stamp replay guard (one mint = one device record), documented in the spec.
 - Two live unauthenticated probes against Apple succeeded: both bag endpoints return plists this stack parses, and certificate pinning validates Apple's real TLS chains. A drift check ships with the repo (`:engine:runProbe`).
 - The courier's auth model is settled: the packed path needs no client certificate; the legacy path answers the handshake with a TLS 1.3 post-handshake `certificate_required` alert.
-- The ADI anisette chain is reimplemented natively, no emulation or helper binary: the white-box OTP ciphers, the GSA provisioning exchange, the full spim/cpim/ptm wire framing, and the validation-stamp ("NAC") mint — pear white-box cipher, blob assembly, and the 16-byte OTS signature (`NacSign`) — are transcribed clean-room from analysis of a compiled ADI implementation, verified byte-exact against oracle vectors and live captures (three genuine provisioning runs plus validation-stamp captures under an instrumented debugger). Every byte group of the exchange and of the 517-byte stamp is identified and reproduced; the full stamp computes byte-exact in Kotlin from its inputs (the earlier python reference model is retired to dev capture notes; the Kotlin port is pinned by synthetic-vector tests against it). 209 tests green, spec rev 34. A minimal public facade (`NacMint`) exposes the mint for consumers. Of the five wire-input mappings from the validation exchange (§1.1 C56), four are live-pinned (pear key, session blob, RNG pads, cert tail); the last gate is the step-2 request blob's field map (C56-a) — ~85% pinned (RSA-OAEP of the pear key + an HMAC key, an HMAC-SHA1 tail, one 32-B pear-AES field and one 20-B slot remain), with the two unpinned sub-fields named in the spec. No anisette server, no Unicorn, no Mac relay.
+- The ADI anisette chain is reimplemented natively, no emulation or helper binary: the white-box OTP ciphers, the GSA provisioning exchange, the full spim/cpim/ptm wire framing, and the validation-stamp ("NAC") mint — pear white-box cipher, blob assembly, and the 16-byte OTS signature (`NacSign`) — are transcribed clean-room from analysis of a compiled ADI implementation, verified byte-exact against oracle vectors and live captures (three genuine provisioning runs plus validation-stamp captures under an instrumented debugger). Every byte group of the exchange and of the 517-byte stamp is identified and reproduced; the full stamp computes byte-exact in Kotlin from its inputs (the earlier python reference model is retired to dev capture notes; the Kotlin port is pinned by synthetic-vector tests against it). 213 tests green, spec rev 35. A minimal public facade (`NacMint`) exposes the mint for consumers. All five wire-input mappings from the validation exchange (§1.1 C56) are now pinned: the step-2 request blob (C56-a) was closed by direct in-process replay of the reference client's validation context — the full 338-byte recipe (constant header, the RSA-OAEP of the pear key + an HMAC key, a fresh 16-byte slot, the length marker, the substituted-and-encrypted 32-byte field, the HMAC-SHA1 tail) is implemented in Kotlin (`NacRequestBlob`) and verified byte-exact on two independent runs. The last gate before a live validation mint is the hardware-identity serialization's field values (C56-c). No anisette server, no Unicorn, no Mac relay.
 
 Not validated yet:
 
diff --git a/docs/imessage-protocol-spec.md b/docs/imessage-protocol-spec.md
index 1439a0f..eb6f769 100644
--- a/docs/imessage-protocol-spec.md
+++ b/docs/imessage-protocol-spec.md
@@ -1,6 +1,6 @@
 # iMessage protocol spec (clean-room)
 
-**Status:** draft — revision 32. The full revision history is at the bottom ([Revision history](#revision-history)); the sections below state the facts as of rev 31.
+**Status:** draft — revision 35. The full revision history is at the bottom ([Revision history](#revision-history)); the sections below state the facts as of rev 31.
 
 **Firewall rule:** this document contains facts only — no code, no function/type names, no copied expression from any reference implementation. Wire-format field names are quoted as on-the-wire protocol data (observable in captures, capture-arbitrated), never as source expression. Facts derived from SSPL/AGPL sources are used facts-only; nothing from them is reproduced. Where the source-derived fact sets agree, the fact is stated once with both citations; where they disagree, the disagreement is stated and tagged `TODO(capture):` — running mitmproxy captures arbitrate. All `TODO(capture)` items are collected in §7.
 
@@ -21,7 +21,7 @@
 - Current shipped flow (OpenBubbles, 2026): the Mac-side helper (`Mac-Hardware-Info` 1.2.0, notarized) only *reads* the machine identifiers — serial, board ID, model, etc. — via public IORegistry/sysctl APIs (docs: "High Sierra and above", no upper macOS version bound) and exports them as a shareable code (≤ 20 users per code, optional one-time-use/48-hour mode); it never invokes an Apple private framework [OB-MHI], [OB-FAQ]. The client then performs the three-step exchange above itself, in software, keyed with those identifiers and paired with an Apple-Account login — the [JJ] emulation path with an official identifier-export helper in front of it. `TODO(capture):` **C56** — the client-side generation procedure behind the three-step exchange: what the client computes with the `id-initialize-validation` session info (the key-establishment math and blob assembly), how it interacts with the Apple-Account/GSA login and the anisette header set (C6) at activation time, and which pieces are fixed protocol constants vs per-account/per-session state. — 2026-09-10: steps 1–2 of C56 are recorded (bullet above); step 3 — key establishment + signing — is closed source: the public OpenAbsinthe-Stub repo is an official mock whose methods are stubs (its README states the real repository is closed source), so the spec records only the API contract: context creation consumes the certificate chain + hardware configuration and outputs the session-info-request blob; key establishment consumes the server response; signing produces the final blob with no further inputs (all state retained in the context) [RP:macos.rs], [RP:activation.rs], [RP:auth.rs], [OA]. Remaining: wire-verification of the blob against one live activation; the enc-variant derivation rides C57. — 2026-09-11 (rev 14 extraction): the five obfuscation labels are now MAPPED to their fields (previously only listed together): serial → `Gq3489ugfi`, platform UUID → `Fyp98tpgj`, root-disk UUID → `kbjfrfpoJU`, ROM → `oycqAZloTNDm`, MLB → `abKPld1EcMni` [OA:nac.rs]; the derivation producing each `_enc` byte variant is still closed source. The hardware-configuration field set is recorded in full: product name (Apple product-type form, e.g. `Macmini9,1`), MAC address (exactly 6 raw bytes), platform serial, platform UUID, root-disk UUID, board ID, OS build number, ROM (raw bytes), MLB, plus the five `_enc` raw-byte variants [OA:nac.rs]. Step 3's closure is confirmed at the source level: the crate holding the key-establishment math ships as a closed-source stub whose mock methods panic; only the API contract is observable [OA:README.md], [OA:nac.rs].
 - The helper's export-code format (2026-09-11, rev 15 — **C58 closed** by facts-only extraction from the helper's public upstream repo, which is unlicensed — facts only): the payload is a 4-byte ASCII magic `OABS`, a one-byte flag (1 = "prevent sharing" mode, 0 otherwise), then a raw protobuf message (no length prefix; protobuf starts at offset 5). Protobuf field map: outer — 1 nested identifier message, 2 macOS product version (sysctl `kern.osproductversion`), 3 protocol version (hardcoded `1640`), 4 device id (the IOPlatformUUID again), 5 a hardcoded iCloudHelper user-agent string, 6 a hardcoded AOSKit version string; nested identifier message — 1 product name (e.g. `MacBookPro18,3`), 2 MAC address (6 raw bytes), 3 platform serial, 4 platform UUID, 5 root-disk UUID, 6 board ID (Apple Silicon: literal prefix `Mac-` + lowercase hex of the device-tree board-id bytes), 7 OS build number (sysctl `kern.osversion`), 8/9/10/12/14 the five `_enc` obfuscated blobs read from the `IOPower:/` registry under Apple's key names (`Gq3489ugfi` serial, `Fyp98tpgj` platform UUID, `kbjfrfpoJU` root-disk UUID, `oycqAZloTNDm` ROM, `abKPld1EcMni` MLB — matching §1.1's label mapping), 11 ROM (Intel: the device-tree options ROM value; Apple Silicon: last 6 bytes of SHA-256 of `/chosen` `unique-chip-id`), 13 MLB string. Two delivery modes: plain = standard base64 of the payload (clipboard text, or the raw payload bytes as a QR code at medium error correction); restricted = AES-256-CBC/PKCS7 over the payload, ciphertext prefixed with ASCII `Salted__` + 8-byte random salt (legacy OpenSSL `enc` container), key/IV derived by the legacy EVP_BytesToKey KDF (repeated MD5 of previous-hash ‖ password ‖ salt to 48 bytes: first 32 = key, next 16 = IV) keyed by a human activation code (`MB` + 4×4 chars from the alphabet `ABCDEFGHJKLMNPQRSTUVWXYZ123456789`), then base64. The restricted mode additionally uploads the blob (JSON `data` + `id` = lowercase hex SHA-256 of the activation code) to the vendor's server (`hw.openbubbles.app/code`) — the ≤20-user/one-time/48-hour mechanics live SERVER-side; nothing is embedded in the payload (no checksum, signature, compression, or expiry). No public parser exists (the client apps are closed-source); the construction above is the parse specification [MHG:ViewController.swift], [MHG:HwIdentifiers.swift], [MHG:mac_hw_info.pb.swift].
 - The validation blob is submitted as the `validation-data` field of the IDS register body and, base64, in the `X-Mme-Nas-Qualify` header of the iCloud account login [RP:ids/user.rs], [RP:auth.rs]. `TODO(capture):` C5 — exact byte shape of the blob a genuine Mac produces, and the current exchange over the two validation bag URLs. — 2026-10-04 (rev 26, live): **REPLAY GUARD — one mint = one device record.** Apple keys a validation blob's consumption server-side: re-submitting an already-consumed blob at the sign-in/register pair answers HTTP 409, which is a REPLAY refusal, NOT a blob rejection — a fresh blob under the same device identity succeeds where the reused one failed, and a captured blob of external provenance succeeds outright (session 17: a captured stamp replaced the local mint and the 409 vanished). Client consequences: mint or fetch a fresh blob per registration attempt (the 15-minute validity above makes stale reuse doubly fatal), and mint the sign-in's blob AT SIGN-IN TIME — never a login-start blob carried across the 2FA wait. A caller-injected blob from any source (local mint, relay Mac, staged capture) is a legitimate stamp; the injection points are the register body's `validation-data` and the sign-in's `X-Mme-Nas-Qualify` header.
-- Hardware-related anisette headers seen in activation flows: `X-Apple-I-SRL-NO` (serial), `X-Apple-I-MLB` (logic-board serial), `X-Apple-I-ROM` (hex ROM, lowercase) [RP:relay.rs], [APA:anisette]. `TODO(capture):` C6 — the full anisette header set a current client actually sends, including which optional hardware headers appear. — 2026-09-10: the header-set half of C6 is closed by facts-only extraction: per-request anisette headers `X-Apple-I-Client-Time`, `X-Apple-I-TimeZone`, `X-Apple-Locale`, `X-Apple-I-MD-RINFO`, `X-Mme-Device-Id`, `X-Apple-I-MD` (base64 OTP), `X-Apple-I-MD-M` (base64 machine ID), plus per-platform hardware headers — macOS: `X-Apple-I-MLB`, `X-Apple-I-ROM` (lowercase hex), `X-Apple-I-SRL-NO` [APA:omnisette], [APA:icloud-auth], [RP:relay.rs]. They are produced by an ADI provisioning exchange with gsa.apple.com (start/finish provisioning returning machine tokens), then a local OTP [APA:omnisette]. GSA context (cross-referenced with C6): the Albert activation itself needs NO Apple-Account login — only the FairPlay-signed activation-info plist (§1.2); the GSA login (full Apple-ID password, SRP over gsa.apple.com/grandslam/GsService2, s2k/s2k_fo PBKDF2, 2FA-capable) feeds the delegate logins that yield the IDS `auth-token`/`profile-id` and the PET token [RP:auth.rs], [APA:icloud-auth]. The extraction confirms the validation blob rides base64 in the `X-Mme-Nas-Qualify` header of the iCloud sign-in POST (recorded above) [RP:auth.rs]. — 2026-09-11 (rev 14 extraction round over the anisette crates): the value-format and provisioning halves of C6 are closed. Per-request value forms: `X-Apple-I-Client-Time` = UTC now truncated to whole seconds, RFC 3339/ISO-8601 with the offset suffix replaced by `Z` (provisioning requests send the raw offset form without the Z — a recorded inconsistency between code paths); `X-Apple-I-TimeZone` = literal `UTC` (not the device zone); `X-Apple-Locale` = `en_US` hardcoded (a companion `X-Apple-I-Locale: en_US` variant exists on the browser-style header set); `X-Apple-I-MD-RINFO` = verbatim passthrough of the string returned in the finish-provisioning response; `X-Mme-Device-Id` = lowercase hyphenated UUID string of 16 locally random bytes (`keychain_identifier`); `X-Apple-I-MD-M` = base64 (standard, padded) of the 60-byte `mid`; `X-Apple-I-MD-LU` = lowercase hex (no dashes) SHA-256 over the same 16 bytes (real macOS instead uses AuthKit's local-user UUID) — present in some header sets, omitted in others (disagreement — C57). Header sets are cached 60 s; a fresh OTP is generated per cache miss. The ADI provisioning flow: `GET https://gsa.apple.com/grandslam/GsService2/lookup` → XML plist whose `urls` keys `midStartProvisioning`/`midFinishProvisioning` give the endpoint URLs (never hardcoded); POST to the start URL with an XML plist body of two empty top-level dicts `Header` and `Request` → response `Response` → `spim` (base64); a local session is built from `spim` (+ empty hostuuid, DSID `-2`, flavor `Mac`=1 / `IOS`=3, flavor chosen by whether the client-info string contains `iPhone OS`) yielding `cpim` (base64); POST to the finish URL with `Request` = {`cpim`} → response `Response` → `ptm`, `tk` (both base64) and `X-Apple-I-MD-RINFO`; finishing the session with the decoded `tk`/`ptm` yields the machine state: `client_secret` (32 bytes), `mid` (60 bytes, Apple-issued at provisioning — reused for every OTP until re-provisioning, which happens only on a not-provisioned failure, e.g. ADI error -45061), `metadata` (variable blob). Provisioning HTTP specifics: `Content-Type: application/x-www-form-urlencoded` despite the XML-plist body (intentional), title-cased header names forced, HTTP/1.1, Apple root CA pinned (embedded DER), and a fixed companion header set on all three requests: akd `User-Agent`, `X-Apple-Baa-E: -10000`, `X-Apple-Baa-Avail: 2`, `X-Apple-Baa-UE: AKAuthenticationError:-7066|com.apple.devicecheck.error.baa:-10000`, `X-Apple-Host-Baa-E: -7066`, `X-Apple-Client-App-Name: akd`, `Accept: */*`, `Accept-Language: en-US,en;q=0.9`, plus `X-Apple-I-MD-LU`, `X-Mme-Device-Id`, `X-Mme-Client-Info`, `X-Apple-I-Client-Time` and any caller-supplied hardware headers. State persists as an XML plist with `keychain_identifier` (data) + the provisioned fields (`client_secret`, `mid`, `metadata`, `rinfo`, `flavor`) [APA:omnisette]. CLOSED-SOURCE RESIDUE: the OTP (`X-Apple-I-MD`) and trusted-device 2FA-code derivations live inside a closed-source crate — its public repo is a stub with `todo!()` methods; recorded is only the call contract: inputs (32-byte `client_secret`, 60-byte `mid`, `metadata`, flavor) → raw OTP bytes (base64 into the header) / 32-bit 2FA code [OA-stub], [APA:omnisette]. — rides C57/C56 residue; the seam stays injectable in the code. — 2026-10-07 (rev 27, clean-room RE of the OpenBubbles ADI library — unstripped Linux `.so`, oracle-verified; the derivation is no longer closed residue): the OTP is fully local and pure. `gen = unix_seconds / 30`; dispatch by OTP flavor byte: 1 (IOS) → `gen_otp` (0x17fba60), 0 (Mac) → `gen_otp_ios` (0x1801d90) — the binary's naming is inverted relative to the flavor (a distinct numbering from the §1.1 session flavor `Mac`=1/`IOS`=3). Cipher inputs: `one` = the machine's `client_info` (required ≥ 0x190 B IOS / ≥ 0xd0 B Mac, length-checked) and `two` = the 32-byte `mid`; output 16 bytes. The wire `X-Apple-I-MD` frame is 28 B: `u32be(5)` ‖ `u32be(16)` ‖ sig16 ‖ `u32be(flavor)`. The 2FA code is `SHA-1(sig16 ‖ secret60) mod 1_000_000` over the machine's full 60-byte secret slice (`machine[0x38..0x74]`; two standard SHA-1 blocks — an earlier report's "48-byte" reading is wrong, 0x18013a2/0x18013bb/0x18013ef). Provisioning framing, asm-pinned: `spim` = `field1` u32 BE @0 ‖ payload-length u32 BE @4 ‖ payload @8 (payload must exceed 59 B, 0x17efb33; more than 23 trailing bytes rejected with error 0x41); `cpim` = 9 fields (u32be(32) ‖ `encsec(rng2)` 32 B ‖ u32be(32) ‖ rng1 32 B ‖ 60 B blob = caller-extra ‖ rng3 pad ‖ u64 BE of arg9 = −2 ‖ u32 BE of the byte-swapped LE dword at rng3[8..12] ‖ two 256-bit tail fields fed by `encrypt(session, rng16, data)` + `spim_map_signature` — the tail's exact wire assembly is `TODO(capture)`); `ptm` is lenient (u32 BE then the whole tail — every candidate shape accepted, error 0); finish requires `tk` exactly 16 B (error 0x8, 0x17f1f11), key16 = `encrypt(session, NULL iv, tk)` (0x17f1eac), decrypt block count = payload.size/16 (0x17f2548), yielding the 0x78-byte provisioned struct (+0x00 16 B, +0x10 u64, +0x18 u64, +0x20 16 B, +0x30..0x70 64 B metadata, +0x70 u32, +0x74 u8 flavor — which bytes are `client_secret` vs `mid` vs `metadata` is `TODO(capture)`). Kotlin: `registration` module `ClearAdiOtp`/`ClearAdiProvision`/`ClearAdiFraming`/`ClearAnisetteProvider`, 192 tests green incl. byte-exact oracle vectors. — 2026-10-07 (rev 28, live capture: one real OpenBubbles provisioning run under gdb, `registration/dev/clearadi/captures/WIRE-NOTES.md`; the framer is corrected): `spim` trailing is NOT capped at 23 B — the live spim carries 99 trailing bytes and parses fine (the earlier 0x41 pin was a probe-harness artifact); the trailing is server material the client relays. `cpim` = an OUTER 276-B message `[u32be(5)][iv 16][u32be(160)][encout 160][X 32][u32be(52)][u32be(4)][Y 52]` whose 160-B encrypt plaintext = `u32be(32) ‖ encsec(rng2) ‖ u32be(32) ‖ rng1 ‖ 60 B blob (caller-extra ‖ rng3 pad) ‖ u64 BE arg9 = −2 (live-confirmed) ‖ u32 BE unix-seconds ‖ u32be(1) ‖ 12 B (source TODO)`; the iv is 16 plain RNG bytes — the earlier 'IV assembled from the Spim's trailing fields' reading was actually the thread-RNG pool (words at r14+0x10, cursor at r14+0x110). `spim_map_signature` (0x17fe2a0) args are (rdi = in, rsi = out): the live call signs a constant 16-B block `e955a4f0…` → `f877c30e…`, and NEITHER that signature nor the SHA-256(encout) digest appears anywhere in the captured wire — the §6 'two 256-bit tail fields' reading is falsified. The `[u32be(52)][u32be(4)][Y 52]` group is the spim's trailing[16:76] relayed verbatim; X (32 B) = `TODO(capture)`. `ptm` = `[u32 BE 4][seed 16][u32 BE payloadLen][payload][tail]` (live 503 B: seed = ptm[4:20] feeds decryptPTM as its chain seed via rcx; block count = payloadLen/16 = 28); key16 = `encrypt(session, NULL iv, tk)` confirmed byte-exact against the live call. ProvisionedData = the 0x78-B Rust struct `{metadata: Vec (400 B live = decrypt out[4:404], length u32 BE at out[0]), client_secret = rng2 (32 B), mid = rng3 (60 B), flavor u8 (0x01 on a live Mac run — distinct from the OTP flavor numbering)}`; the finish gate is the decrypt output's **out[408:440] == rng1 echo** (NOT out[0:32]); the OTP-path report's ProvisionedMachine note (mid[32]@+0x18, secret[60]@+0x38) had the two swapped. Kotlin `ClearAdiFraming`/`ClearAnisetteProvider` restructured to the live shapes; 194 tests green. Remaining `TODO(capture)`: the X32 source, the 12-B plaintext tail, trailing[0:16]'s role. — 2026-10-07 (rev 29, continuation capture — two further live provisioning runs, `gdb_prov8/9.gdb`, byte-exact on both): the three remaining cpim TODOs are CLOSED. X = SHA-256(encout ‖ spim_map_signature(trailing[0:16]) ‖ a fixed 24-byte filler constant `3795020c05f77009cbfeaa78a5bcb3175bad60b9deaaaa8d` (.so .rodata) — the digest is written to the wire byte-exact as the `[X 32]` group, so the rev-28 "sig16 and the digest appear nowhere on the wire" note resolves: both are on the wire transitively (sig16 as the hash input, the digest as X). The signature's INPUT is NOT a constant block — the "constant e955a4f0…" seen in the morning runs was that session's trailing[0:16]; the trailing head is server material that differs between provisioning sessions, and the signature model still reproduces the live output exactly. The 12-B plaintext tail = 12 fresh RNG bytes (low bytes of 12 thread-RNG pool words drawn immediately before the IV's 16 — the same construction as the IV, so the framer draws 12). Kotlin: the pinned production seal (`CpimShaTailSeal` — SHA-256 via the platform, sig via the ported `spimMapSignature`) is the provider default; 195 tests green. — 2026-10-08 (rev 30, clean-room RE of the NAC mint — the validation blob "C5" — over the same unstripped Linux `.so`; gdb oracle quadruples first, then python model, then Kotlin; method + findings in `registration/dev/clearadi/captures/NAC-NOTES.md`): the mint is local and pure, and every byte of the 517-B validation stamp is now derived EXCEPT one residue (below). The stamp = `0x02 ‖ rand16 (RNG) ‖ sig16 ‖ u32be(0x1e0) ‖ blob480`; blob480 = `tag 0x05 ‖ u32be(1) ‖ u32be(0x180) ‖ scramble_body(session250, rng_pad130) ‖ u64be(79) ‖ cert79`, where cert79 is the first 79 B of the ctx cert chain and session250 the 250-B session slice — E2E the full stamp computes byte-exact from (cert79, session250, rng_pad130, body576, rand16). The crypto layers, all byte-exact vs three independent live runs: **pear_aes** — a white-box AES variant (`create_rounds` = AES-128-style expansion with pluggable sbox/rcon; `init_key` = S1-scramble → schedule; `establish_key` = schedule + T-transform of blocks 1–9 only, blocks 0/10 raw; `encrypt_cbc` = whitening + **9 rounds** + final `SE[st9[p]]^rk11` with p=[12,10,4,3,15,5,2,8,14,1,9,7,0,13,11,6]; `decrypt_cbc` = backward rounds with the key xor fused into the table index, final `perm(SDI[st9^rk1])^chain^rk0`); **domergestep2** — the white-box core of `scramble_body` (KP key schedule over 80 B, 4 blocks of the `0x51·m` constant with state[0] xored on EVERY block, final `TC[x]+k`, out = state ⊕ in1; 21/21 live captures); **key_establishment** — the EstablishKeyResponse wire is `tag ‖ key16@0x01 ‖ u32be bodyLen@0x11 ‖ body@0x15 (0x250) ‖ trailing (85 B, unused by the crypto)`. **SignState::sign** (the 16-B OTS signature over the blob): structure fully decoded — scatter → polynomial chain → flag table → u32 permutations → divisor table → key map → keygen → matrix/phases B–F → 16 position rounds → tail (fold chains + threshold cipher + staging + final formula); stages 1–9 are hand-transcribed and byte-exact vs ground truth, the tail's threshold cipher (AES-like, 9 rounds × 30 generator runs) is structurally decoded with 270 checkpointed rounds, and the signature the model produces is byte-exact vs the live stamp. CLOSED (same day, follow-up): the capture-free pure-code transcription of the tail cipher and the pre-init region — the full 517-B stamp now computes byte-exact from (cert79, session250, rng_pad130, body576, rand16) in a pure-Python model (no emulator, no captures; `sig_hand.py verify` 20/20) with the complete constant inventory recorded for the Kotlin port (see WORKLOG session 20). Kotlin: `registration` `PearTablesData`/`PearTables` (generated base64 table image, ClearAdiTablesData pattern), `PearAes`, `NacMerge`, `NacValidation` (`mint` + `keyEstablishment`; sig16 a parameter — no placeholder signature), 206 tests green (synthetic vectors, no Apple bytes). — 2026-10-08 (rev 31, Kotlin port of the sign model — the sig16 residue above is CLOSED): `SignState::sign` is transcribed to `registration` `NacSign` (full pipeline: scatter → u32 flag table → perms → divisor/key map → keygen → matrix/phases B–E → 16 position rounds, then the 30-run tail — RS32/rec0/r70ab init, run-start feedback, soup57/soup80, the 9-round threshold cipher, staging from the generator soup, final formula, chain1 fold), with its .rodata tables embedded as a generated base64 image (`NacSignTablesData`/`NacSignTables`, PearTablesData pattern; the 17-loop byte tables are in-range slices of the T2_BIG span). `NacValidation.mint(cert79, session250, rngPad130, rand16, body576)` now computes the full 517-B stamp including sig16 internally (the sig16-parameter assembly step remains as `mintWithSig`); Kotlin sign == python model on LCG-seeded synthetic vectors (incl. zero-rand16 and zero-blob edges), full-mint e2e byte-exact, 208 tests green. — 2026-10-08 (rev 32, three instrumented live runs of the same OpenBubbles app under gdb — the mint's INPUT mappings (C56-b/c/d/e + cert79) are now wire-pinned, and a live-input divergence in the rev-30/31 sign model is discovered; dumps + method in `registration/dev/clearadi/captures/NAC-NOTES.md` session-21 continuation): the five mint inputs map from the exchange as follows — **C56-b pearKey16** = 16 fresh client RNG bytes created inside `ValidationCtx::new` (rand-crate `[u8;16]` sample; wrapped to the server inside the step-2 request blob, which is why it never appears in the session-info response); **C56-c session250** = the 250-B `HardwareConfig::to_bin` output — the client's hardware-identity serialization (model identifier, serial, platform-UUID + second UUID, board-id `Mac-…`, OS build, MLB — ASCII, len-prefixed), held at ctx+0x20 and NOT a slice of any server response; **C56-d rngPad130** = 130 fresh thread-RNG bytes filling the 0x180-B scramble buffer after `u32be(len) ‖ data` (pad content is irrelevant filler, drawn fresh per mint); **C56-e body576** = the SDAT-mapped decrypt of the session-info response's `body@0x15` (0x250 B) region `[2:578]` — i.e. ctx[0x40:0x280]; and **cert79 is NOT the step-1 certificate** (the rev-30 reading is falsified): it is the first 0x4f bytes of the response's 85-B trailing Vec (ctx+0x00), server material relayed into the stamp — wire-verified ×3 (stamp[438:517] == trailing[0:79]). The step-2 request blob itself is now wire-captured: 338 B = constant header `01 08 4b2c91481d9b7da0` + 328 B per-session material (RSA-OAEP under the step-1 cert's public key + digests, built inside `ValidationCtx::new`, held at ctx+0x2c0) — its exact field map and the HardwareConfig serialization grammar remain `TODO(capture)` (C56-a/C56-c). **Live-input divergence (new residue):** with ALL FOUR `sign::sign` args byte-verified against the captured call (rsi=body576, rdx=rand16, rcx=blob480), the rev-30/31 pure model produces a WRONG sig16 on two independent fresh runs (e.g. `7a9555e5…`/`b2c72389…` vs live `0160f19c…`) while still reproducing the session-20 capture byte-exact — the empirical tail-cipher/initial-carry fit contains an input-dependent path that the session-20 data never exercised; a live mint is blocked on closing this, and the rev-30/31 "byte-exact" claims hold only for the session-20 capture and the synthetic vectors. Kotlin: `NacValidation.keyEstablishmentFull` (payload + trailing), `NacMint` facade updated with the pinned mappings; 209 registration tests green. — 2026-10-09 (rev 33, the sign-model fresh-input divergence is CLOSED — the live-mint blocker from rev 32 is gone; method + dumps in `registration/dev/clearadi/captures/NAC-NOTES.md` session-23 continuation): the divergence was two more session-20-frozen constants inside `SignState::sign`, both found by rebuilding a fresh-input round-state checkpoint harness (`gdb_c56d.gdb`, 270 round dumps in `captures/c56d/`) and diffing stage-by-stage against a unicorn execution of the same input (the emulator reproduces the live sig16 byte-exact, so the fit — not the emulator — was wrong). (1) **staging i==10 ecx2**: the staging maze's i==10 branch multiplies in `perm2u[st[0x6fa2]]` (rsp+0x28, loaded at 0x17a36c0 from state+0x6fa2); the fitted `perm2u[0x40]` was the session-20 snapshot (s20 st[0x6fa2]==0x40 — a no-op there, silently wrong elsewhere). (2) **the P region (state+0x6898, 7×256) is INPUT-DEPENDENT** — the "runtime constant, byte-identical across base/mod/body-flip" reading (rev 30) is falsified: the SSE builder at 0x17a1381-0x17a20b5 parameterizes five of the seven 256-byte tables on five body-derived bytes (`st[0x288a]^st[0x287a]`, `st[0x287f]^st[0x267f]`, `st[0x2683]^st[0x2753]`, `st[0x287d]^st[0x288d]`, `st[0x274b]^st[0x288b]`); tables 2/5 are the only true constants. The builder's instruction stream is serialized and re-executed lane-wise (generated `NacPTable.kt`, 1833 ints + 46 const vectors), verified byte-exact vs the emulated builder on the fresh input, two random states and the session-20 capture. Also pinned while re-diffing: the region-0x6f98 sel bytes, 0x6fd8 selectors (base-7 digits of `body[0xe0+i]^body[0xf0+i]`), 0x6fe8/0x6fec masks/flags, the scatter N and the map-key cursor are all body-derived (already fixed in-session in the python model; now ported), and the cipher's round "RC constants" are the state's own 0x25d8 words. Verification: the pure model + Kotlin `NacSign` reproduce the FRESH live sig16 `307d7151…` and the FULL fresh 517-B stamp byte-exact (`captures/c56d/fresh_stamp.bin`), the session-20 stamp still byte-exact, `sig_hand.py verify` 20/20; Kotlin: `NacSign` re-ported (region6f98/masks/sel/N/cursor/scatter-mutated/RC now computed; the four former state-embedded constants dropped from `NacSignTablesData`), 209 registration tests green (vectors regenerated), imessage `:server:testDebugUnitTest` green. Remaining before a live attempt: C56-a (request-blob field map) + C56-c (HardwareConfig grammar) — both `TODO(capture)`, C58 OABS parser. — 2026-10-09 (rev 34, C56-a request-blob field map ~85% pinned — four further instrumented runs, `gdb_c56e..h.gdb`, dumps in `captures/c56e..h/`, write-up in NAC-NOTES.md session-24 continuation): the 338-B step-2 request blob = constant header `01 08 4b2c91481d9b7da0` ‖ [10:266] = 256-B **RSA-2048-OAEP-SHA1** ciphertext under the step-1 cert's public key (no sha2 crate linked in the helper binary; a single `Oaep::new` monomorphization; output 0x100 checked in the disasm), plaintext = **pearKey16 ‖ hmacKey20** (36 B — the encrypt's r9=0x24; hmacKey byte-verified at plaintext offset 16 on two runs) ‖ [266:286] = 20 B, UNPINNED (ends with `u32be(32)`, a length marker for the next field; assembly source = struct+0x450 ← [rsp+0x260] + r15d) ‖ [286:318] = 32 B = the serialize-time content of the `encrypt_cbc` output Vec (the serializer reads the Vec the encrypt_cbc sret was moved into; offline pear-AES reproduction from (plaintext32, iv, rk176) is open — the plaintext carries a 0x72-fill pattern suggesting a reused/padded scratch struct) ‖ [318:338] = **HMAC-SHA1(hmacKey20, the 32-B field)** — VERIFIED byte-exact: the two digest finalizes are the inner/outer of a standard HMAC-SHA1 (inner = sha1(key⊕ipad ‖ msg), outer = sha1(key⊕opad ‖ inner); the 20-B key = u1[0:20]^0x36 == u3[0:20]^0x5c). Role model: the server decrypts the OAEP → (pear16, hmacKey), derives the PAESKey from pear16 (`init_key` input confirmed = pear16), decrypts the 32-B field, and verifies the HMAC — a possession-of-pear16 proof bound to the blob. Also pinned: the blob Vec at ctx+0x2c0 is already moved-out by key_establishment time — capture it at the serializer return (0x1794998, sret {tag=6, cap, ptr@[0xc8], len@[0xd0]=0x152}) instead. Remaining for C56-a closure: the 20-B slot's source and the 32-B field's derivation.
+- Hardware-related anisette headers seen in activation flows: `X-Apple-I-SRL-NO` (serial), `X-Apple-I-MLB` (logic-board serial), `X-Apple-I-ROM` (hex ROM, lowercase) [RP:relay.rs], [APA:anisette]. `TODO(capture):` C6 — the full anisette header set a current client actually sends, including which optional hardware headers appear. — 2026-09-10: the header-set half of C6 is closed by facts-only extraction: per-request anisette headers `X-Apple-I-Client-Time`, `X-Apple-I-TimeZone`, `X-Apple-Locale`, `X-Apple-I-MD-RINFO`, `X-Mme-Device-Id`, `X-Apple-I-MD` (base64 OTP), `X-Apple-I-MD-M` (base64 machine ID), plus per-platform hardware headers — macOS: `X-Apple-I-MLB`, `X-Apple-I-ROM` (lowercase hex), `X-Apple-I-SRL-NO` [APA:omnisette], [APA:icloud-auth], [RP:relay.rs]. They are produced by an ADI provisioning exchange with gsa.apple.com (start/finish provisioning returning machine tokens), then a local OTP [APA:omnisette]. GSA context (cross-referenced with C6): the Albert activation itself needs NO Apple-Account login — only the FairPlay-signed activation-info plist (§1.2); the GSA login (full Apple-ID password, SRP over gsa.apple.com/grandslam/GsService2, s2k/s2k_fo PBKDF2, 2FA-capable) feeds the delegate logins that yield the IDS `auth-token`/`profile-id` and the PET token [RP:auth.rs], [APA:icloud-auth]. The extraction confirms the validation blob rides base64 in the `X-Mme-Nas-Qualify` header of the iCloud sign-in POST (recorded above) [RP:auth.rs]. — 2026-09-11 (rev 14 extraction round over the anisette crates): the value-format and provisioning halves of C6 are closed. Per-request value forms: `X-Apple-I-Client-Time` = UTC now truncated to whole seconds, RFC 3339/ISO-8601 with the offset suffix replaced by `Z` (provisioning requests send the raw offset form without the Z — a recorded inconsistency between code paths); `X-Apple-I-TimeZone` = literal `UTC` (not the device zone); `X-Apple-Locale` = `en_US` hardcoded (a companion `X-Apple-I-Locale: en_US` variant exists on the browser-style header set); `X-Apple-I-MD-RINFO` = verbatim passthrough of the string returned in the finish-provisioning response; `X-Mme-Device-Id` = lowercase hyphenated UUID string of 16 locally random bytes (`keychain_identifier`); `X-Apple-I-MD-M` = base64 (standard, padded) of the 60-byte `mid`; `X-Apple-I-MD-LU` = lowercase hex (no dashes) SHA-256 over the same 16 bytes (real macOS instead uses AuthKit's local-user UUID) — present in some header sets, omitted in others (disagreement — C57). Header sets are cached 60 s; a fresh OTP is generated per cache miss. The ADI provisioning flow: `GET https://gsa.apple.com/grandslam/GsService2/lookup` → XML plist whose `urls` keys `midStartProvisioning`/`midFinishProvisioning` give the endpoint URLs (never hardcoded); POST to the start URL with an XML plist body of two empty top-level dicts `Header` and `Request` → response `Response` → `spim` (base64); a local session is built from `spim` (+ empty hostuuid, DSID `-2`, flavor `Mac`=1 / `IOS`=3, flavor chosen by whether the client-info string contains `iPhone OS`) yielding `cpim` (base64); POST to the finish URL with `Request` = {`cpim`} → response `Response` → `ptm`, `tk` (both base64) and `X-Apple-I-MD-RINFO`; finishing the session with the decoded `tk`/`ptm` yields the machine state: `client_secret` (32 bytes), `mid` (60 bytes, Apple-issued at provisioning — reused for every OTP until re-provisioning, which happens only on a not-provisioned failure, e.g. ADI error -45061), `metadata` (variable blob). Provisioning HTTP specifics: `Content-Type: application/x-www-form-urlencoded` despite the XML-plist body (intentional), title-cased header names forced, HTTP/1.1, Apple root CA pinned (embedded DER), and a fixed companion header set on all three requests: akd `User-Agent`, `X-Apple-Baa-E: -10000`, `X-Apple-Baa-Avail: 2`, `X-Apple-Baa-UE: AKAuthenticationError:-7066|com.apple.devicecheck.error.baa:-10000`, `X-Apple-Host-Baa-E: -7066`, `X-Apple-Client-App-Name: akd`, `Accept: */*`, `Accept-Language: en-US,en;q=0.9`, plus `X-Apple-I-MD-LU`, `X-Mme-Device-Id`, `X-Mme-Client-Info`, `X-Apple-I-Client-Time` and any caller-supplied hardware headers. State persists as an XML plist with `keychain_identifier` (data) + the provisioned fields (`client_secret`, `mid`, `metadata`, `rinfo`, `flavor`) [APA:omnisette]. CLOSED-SOURCE RESIDUE: the OTP (`X-Apple-I-MD`) and trusted-device 2FA-code derivations live inside a closed-source crate — its public repo is a stub with `todo!()` methods; recorded is only the call contract: inputs (32-byte `client_secret`, 60-byte `mid`, `metadata`, flavor) → raw OTP bytes (base64 into the header) / 32-bit 2FA code [OA-stub], [APA:omnisette]. — rides C57/C56 residue; the seam stays injectable in the code. — 2026-10-07 (rev 27, clean-room RE of the OpenBubbles ADI library — unstripped Linux `.so`, oracle-verified; the derivation is no longer closed residue): the OTP is fully local and pure. `gen = unix_seconds / 30`; dispatch by OTP flavor byte: 1 (IOS) → `gen_otp` (0x17fba60), 0 (Mac) → `gen_otp_ios` (0x1801d90) — the binary's naming is inverted relative to the flavor (a distinct numbering from the §1.1 session flavor `Mac`=1/`IOS`=3). Cipher inputs: `one` = the machine's `client_info` (required ≥ 0x190 B IOS / ≥ 0xd0 B Mac, length-checked) and `two` = the 32-byte `mid`; output 16 bytes. The wire `X-Apple-I-MD` frame is 28 B: `u32be(5)` ‖ `u32be(16)` ‖ sig16 ‖ `u32be(flavor)`. The 2FA code is `SHA-1(sig16 ‖ secret60) mod 1_000_000` over the machine's full 60-byte secret slice (`machine[0x38..0x74]`; two standard SHA-1 blocks — an earlier report's "48-byte" reading is wrong, 0x18013a2/0x18013bb/0x18013ef). Provisioning framing, asm-pinned: `spim` = `field1` u32 BE @0 ‖ payload-length u32 BE @4 ‖ payload @8 (payload must exceed 59 B, 0x17efb33; more than 23 trailing bytes rejected with error 0x41); `cpim` = 9 fields (u32be(32) ‖ `encsec(rng2)` 32 B ‖ u32be(32) ‖ rng1 32 B ‖ 60 B blob = caller-extra ‖ rng3 pad ‖ u64 BE of arg9 = −2 ‖ u32 BE of the byte-swapped LE dword at rng3[8..12] ‖ two 256-bit tail fields fed by `encrypt(session, rng16, data)` + `spim_map_signature` — the tail's exact wire assembly is `TODO(capture)`); `ptm` is lenient (u32 BE then the whole tail — every candidate shape accepted, error 0); finish requires `tk` exactly 16 B (error 0x8, 0x17f1f11), key16 = `encrypt(session, NULL iv, tk)` (0x17f1eac), decrypt block count = payload.size/16 (0x17f2548), yielding the 0x78-byte provisioned struct (+0x00 16 B, +0x10 u64, +0x18 u64, +0x20 16 B, +0x30..0x70 64 B metadata, +0x70 u32, +0x74 u8 flavor — which bytes are `client_secret` vs `mid` vs `metadata` is `TODO(capture)`). Kotlin: `registration` module `ClearAdiOtp`/`ClearAdiProvision`/`ClearAdiFraming`/`ClearAnisetteProvider`, 192 tests green incl. byte-exact oracle vectors. — 2026-10-07 (rev 28, live capture: one real OpenBubbles provisioning run under gdb, `registration/dev/clearadi/captures/WIRE-NOTES.md`; the framer is corrected): `spim` trailing is NOT capped at 23 B — the live spim carries 99 trailing bytes and parses fine (the earlier 0x41 pin was a probe-harness artifact); the trailing is server material the client relays. `cpim` = an OUTER 276-B message `[u32be(5)][iv 16][u32be(160)][encout 160][X 32][u32be(52)][u32be(4)][Y 52]` whose 160-B encrypt plaintext = `u32be(32) ‖ encsec(rng2) ‖ u32be(32) ‖ rng1 ‖ 60 B blob (caller-extra ‖ rng3 pad) ‖ u64 BE arg9 = −2 (live-confirmed) ‖ u32 BE unix-seconds ‖ u32be(1) ‖ 12 B (source TODO)`; the iv is 16 plain RNG bytes — the earlier 'IV assembled from the Spim's trailing fields' reading was actually the thread-RNG pool (words at r14+0x10, cursor at r14+0x110). `spim_map_signature` (0x17fe2a0) args are (rdi = in, rsi = out): the live call signs a constant 16-B block `e955a4f0…` → `f877c30e…`, and NEITHER that signature nor the SHA-256(encout) digest appears anywhere in the captured wire — the §6 'two 256-bit tail fields' reading is falsified. The `[u32be(52)][u32be(4)][Y 52]` group is the spim's trailing[16:76] relayed verbatim; X (32 B) = `TODO(capture)`. `ptm` = `[u32 BE 4][seed 16][u32 BE payloadLen][payload][tail]` (live 503 B: seed = ptm[4:20] feeds decryptPTM as its chain seed via rcx; block count = payloadLen/16 = 28); key16 = `encrypt(session, NULL iv, tk)` confirmed byte-exact against the live call. ProvisionedData = the 0x78-B Rust struct `{metadata: Vec (400 B live = decrypt out[4:404], length u32 BE at out[0]), client_secret = rng2 (32 B), mid = rng3 (60 B), flavor u8 (0x01 on a live Mac run — distinct from the OTP flavor numbering)}`; the finish gate is the decrypt output's **out[408:440] == rng1 echo** (NOT out[0:32]); the OTP-path report's ProvisionedMachine note (mid[32]@+0x18, secret[60]@+0x38) had the two swapped. Kotlin `ClearAdiFraming`/`ClearAnisetteProvider` restructured to the live shapes; 194 tests green. Remaining `TODO(capture)`: the X32 source, the 12-B plaintext tail, trailing[0:16]'s role. — 2026-10-07 (rev 29, continuation capture — two further live provisioning runs, `gdb_prov8/9.gdb`, byte-exact on both): the three remaining cpim TODOs are CLOSED. X = SHA-256(encout ‖ spim_map_signature(trailing[0:16]) ‖ a fixed 24-byte filler constant `3795020c05f77009cbfeaa78a5bcb3175bad60b9deaaaa8d` (.so .rodata) — the digest is written to the wire byte-exact as the `[X 32]` group, so the rev-28 "sig16 and the digest appear nowhere on the wire" note resolves: both are on the wire transitively (sig16 as the hash input, the digest as X). The signature's INPUT is NOT a constant block — the "constant e955a4f0…" seen in the morning runs was that session's trailing[0:16]; the trailing head is server material that differs between provisioning sessions, and the signature model still reproduces the live output exactly. The 12-B plaintext tail = 12 fresh RNG bytes (low bytes of 12 thread-RNG pool words drawn immediately before the IV's 16 — the same construction as the IV, so the framer draws 12). Kotlin: the pinned production seal (`CpimShaTailSeal` — SHA-256 via the platform, sig via the ported `spimMapSignature`) is the provider default; 195 tests green. — 2026-10-08 (rev 30, clean-room RE of the NAC mint — the validation blob "C5" — over the same unstripped Linux `.so`; gdb oracle quadruples first, then python model, then Kotlin; method + findings in `registration/dev/clearadi/captures/NAC-NOTES.md`): the mint is local and pure, and every byte of the 517-B validation stamp is now derived EXCEPT one residue (below). The stamp = `0x02 ‖ rand16 (RNG) ‖ sig16 ‖ u32be(0x1e0) ‖ blob480`; blob480 = `tag 0x05 ‖ u32be(1) ‖ u32be(0x180) ‖ scramble_body(session250, rng_pad130) ‖ u64be(79) ‖ cert79`, where cert79 is the first 79 B of the ctx cert chain and session250 the 250-B session slice — E2E the full stamp computes byte-exact from (cert79, session250, rng_pad130, body576, rand16). The crypto layers, all byte-exact vs three independent live runs: **pear_aes** — a white-box AES variant (`create_rounds` = AES-128-style expansion with pluggable sbox/rcon; `init_key` = S1-scramble → schedule; `establish_key` = schedule + T-transform of blocks 1–9 only, blocks 0/10 raw; `encrypt_cbc` = whitening + **9 rounds** + final `SE[st9[p]]^rk11` with p=[12,10,4,3,15,5,2,8,14,1,9,7,0,13,11,6]; `decrypt_cbc` = backward rounds with the key xor fused into the table index, final `perm(SDI[st9^rk1])^chain^rk0`); **domergestep2** — the white-box core of `scramble_body` (KP key schedule over 80 B, 4 blocks of the `0x51·m` constant with state[0] xored on EVERY block, final `TC[x]+k`, out = state ⊕ in1; 21/21 live captures); **key_establishment** — the EstablishKeyResponse wire is `tag ‖ key16@0x01 ‖ u32be bodyLen@0x11 ‖ body@0x15 (0x250) ‖ trailing (85 B, unused by the crypto)`. **SignState::sign** (the 16-B OTS signature over the blob): structure fully decoded — scatter → polynomial chain → flag table → u32 permutations → divisor table → key map → keygen → matrix/phases B–F → 16 position rounds → tail (fold chains + threshold cipher + staging + final formula); stages 1–9 are hand-transcribed and byte-exact vs ground truth, the tail's threshold cipher (AES-like, 9 rounds × 30 generator runs) is structurally decoded with 270 checkpointed rounds, and the signature the model produces is byte-exact vs the live stamp. CLOSED (same day, follow-up): the capture-free pure-code transcription of the tail cipher and the pre-init region — the full 517-B stamp now computes byte-exact from (cert79, session250, rng_pad130, body576, rand16) in a pure-Python model (no emulator, no captures; `sig_hand.py verify` 20/20) with the complete constant inventory recorded for the Kotlin port (see WORKLOG session 20). Kotlin: `registration` `PearTablesData`/`PearTables` (generated base64 table image, ClearAdiTablesData pattern), `PearAes`, `NacMerge`, `NacValidation` (`mint` + `keyEstablishment`; sig16 a parameter — no placeholder signature), 206 tests green (synthetic vectors, no Apple bytes). — 2026-10-08 (rev 31, Kotlin port of the sign model — the sig16 residue above is CLOSED): `SignState::sign` is transcribed to `registration` `NacSign` (full pipeline: scatter → u32 flag table → perms → divisor/key map → keygen → matrix/phases B–E → 16 position rounds, then the 30-run tail — RS32/rec0/r70ab init, run-start feedback, soup57/soup80, the 9-round threshold cipher, staging from the generator soup, final formula, chain1 fold), with its .rodata tables embedded as a generated base64 image (`NacSignTablesData`/`NacSignTables`, PearTablesData pattern; the 17-loop byte tables are in-range slices of the T2_BIG span). `NacValidation.mint(cert79, session250, rngPad130, rand16, body576)` now computes the full 517-B stamp including sig16 internally (the sig16-parameter assembly step remains as `mintWithSig`); Kotlin sign == python model on LCG-seeded synthetic vectors (incl. zero-rand16 and zero-blob edges), full-mint e2e byte-exact, 208 tests green. — 2026-10-08 (rev 32, three instrumented live runs of the same OpenBubbles app under gdb — the mint's INPUT mappings (C56-b/c/d/e + cert79) are now wire-pinned, and a live-input divergence in the rev-30/31 sign model is discovered; dumps + method in `registration/dev/clearadi/captures/NAC-NOTES.md` session-21 continuation): the five mint inputs map from the exchange as follows — **C56-b pearKey16** = 16 fresh client RNG bytes created inside `ValidationCtx::new` (rand-crate `[u8;16]` sample; wrapped to the server inside the step-2 request blob, which is why it never appears in the session-info response); **C56-c session250** = the 250-B `HardwareConfig::to_bin` output — the client's hardware-identity serialization (model identifier, serial, platform-UUID + second UUID, board-id `Mac-…`, OS build, MLB — ASCII, len-prefixed), held at ctx+0x20 and NOT a slice of any server response; **C56-d rngPad130** = 130 fresh thread-RNG bytes filling the 0x180-B scramble buffer after `u32be(len) ‖ data` (pad content is irrelevant filler, drawn fresh per mint); **C56-e body576** = the SDAT-mapped decrypt of the session-info response's `body@0x15` (0x250 B) region `[2:578]` — i.e. ctx[0x40:0x280]; and **cert79 is NOT the step-1 certificate** (the rev-30 reading is falsified): it is the first 0x4f bytes of the response's 85-B trailing Vec (ctx+0x00), server material relayed into the stamp — wire-verified ×3 (stamp[438:517] == trailing[0:79]). The step-2 request blob itself is now wire-captured: 338 B = constant header `01 08 4b2c91481d9b7da0` + 328 B per-session material (RSA-OAEP under the step-1 cert's public key + digests, built inside `ValidationCtx::new`, held at ctx+0x2c0) — its exact field map and the HardwareConfig serialization grammar remain `TODO(capture)` (C56-a/C56-c). **Live-input divergence (new residue):** with ALL FOUR `sign::sign` args byte-verified against the captured call (rsi=body576, rdx=rand16, rcx=blob480), the rev-30/31 pure model produces a WRONG sig16 on two independent fresh runs (e.g. `7a9555e5…`/`b2c72389…` vs live `0160f19c…`) while still reproducing the session-20 capture byte-exact — the empirical tail-cipher/initial-carry fit contains an input-dependent path that the session-20 data never exercised; a live mint is blocked on closing this, and the rev-30/31 "byte-exact" claims hold only for the session-20 capture and the synthetic vectors. Kotlin: `NacValidation.keyEstablishmentFull` (payload + trailing), `NacMint` facade updated with the pinned mappings; 209 registration tests green. — 2026-10-09 (rev 33, the sign-model fresh-input divergence is CLOSED — the live-mint blocker from rev 32 is gone; method + dumps in `registration/dev/clearadi/captures/NAC-NOTES.md` session-23 continuation): the divergence was two more session-20-frozen constants inside `SignState::sign`, both found by rebuilding a fresh-input round-state checkpoint harness (`gdb_c56d.gdb`, 270 round dumps in `captures/c56d/`) and diffing stage-by-stage against a unicorn execution of the same input (the emulator reproduces the live sig16 byte-exact, so the fit — not the emulator — was wrong). (1) **staging i==10 ecx2**: the staging maze's i==10 branch multiplies in `perm2u[st[0x6fa2]]` (rsp+0x28, loaded at 0x17a36c0 from state+0x6fa2); the fitted `perm2u[0x40]` was the session-20 snapshot (s20 st[0x6fa2]==0x40 — a no-op there, silently wrong elsewhere). (2) **the P region (state+0x6898, 7×256) is INPUT-DEPENDENT** — the "runtime constant, byte-identical across base/mod/body-flip" reading (rev 30) is falsified: the SSE builder at 0x17a1381-0x17a20b5 parameterizes five of the seven 256-byte tables on five body-derived bytes (`st[0x288a]^st[0x287a]`, `st[0x287f]^st[0x267f]`, `st[0x2683]^st[0x2753]`, `st[0x287d]^st[0x288d]`, `st[0x274b]^st[0x288b]`); tables 2/5 are the only true constants. The builder's instruction stream is serialized and re-executed lane-wise (generated `NacPTable.kt`, 1833 ints + 46 const vectors), verified byte-exact vs the emulated builder on the fresh input, two random states and the session-20 capture. Also pinned while re-diffing: the region-0x6f98 sel bytes, 0x6fd8 selectors (base-7 digits of `body[0xe0+i]^body[0xf0+i]`), 0x6fe8/0x6fec masks/flags, the scatter N and the map-key cursor are all body-derived (already fixed in-session in the python model; now ported), and the cipher's round "RC constants" are the state's own 0x25d8 words. Verification: the pure model + Kotlin `NacSign` reproduce the FRESH live sig16 `307d7151…` and the FULL fresh 517-B stamp byte-exact (`captures/c56d/fresh_stamp.bin`), the session-20 stamp still byte-exact, `sig_hand.py verify` 20/20; Kotlin: `NacSign` re-ported (region6f98/masks/sel/N/cursor/scatter-mutated/RC now computed; the four former state-embedded constants dropped from `NacSignTablesData`), 209 registration tests green (vectors regenerated), imessage `:server:testDebugUnitTest` green. Remaining before a live attempt: C56-a (request-blob field map) + C56-c (HardwareConfig grammar) — both `TODO(capture)`, C58 OABS parser. — 2026-10-09 (rev 34, C56-a request-blob field map ~85% pinned — four further instrumented runs, `gdb_c56e..h.gdb`, dumps in `captures/c56e..h/`, write-up in NAC-NOTES.md session-24 continuation): the 338-B step-2 request blob = constant header `01 08 4b2c91481d9b7da0` ‖ [10:266] = 256-B **RSA-2048-OAEP-SHA1** ciphertext under the step-1 cert's public key (no sha2 crate linked in the helper binary; a single `Oaep::new` monomorphization; output 0x100 checked in the disasm), plaintext = **pearKey16 ‖ hmacKey20** (36 B — the encrypt's r9=0x24; hmacKey byte-verified at plaintext offset 16 on two runs) ‖ [266:286] = 20 B, UNPINNED (ends with `u32be(32)`, a length marker for the next field; assembly source = struct+0x450 ← [rsp+0x260] + r15d) ‖ [286:318] = 32 B = the serialize-time content of the `encrypt_cbc` output Vec (the serializer reads the Vec the encrypt_cbc sret was moved into; offline pear-AES reproduction from (plaintext32, iv, rk176) is open — the plaintext carries a 0x72-fill pattern suggesting a reused/padded scratch struct) ‖ [318:338] = **HMAC-SHA1(hmacKey20, the 32-B field)** — VERIFIED byte-exact: the two digest finalizes are the inner/outer of a standard HMAC-SHA1 (inner = sha1(key⊕ipad ‖ msg), outer = sha1(key⊕opad ‖ inner); the 20-B key = u1[0:20]^0x36 == u3[0:20]^0x5c). Role model: the server decrypts the OAEP → (pear16, hmacKey), derives the PAESKey from pear16 (`init_key` input confirmed = pear16), decrypts the 32-B field, and verifies the HMAC — a possession-of-pear16 proof bound to the blob. Also pinned: the blob Vec at ctx+0x2c0 is already moved-out by key_establishment time — capture it at the serializer return (0x1794998, sret {tag=6, cap, ptr@[0xc8], len@[0xd0]=0x152}) instead. Remaining for C56-a closure: the 20-B slot's source and the 32-B field's derivation. — 2026-10-12 (rev 35, C56-a CLOSED — the step-2 `session-info-request` blob fully derived by direct in-process gdb replay of `ValidationCtx::new` (two byte-verified runs) after the natural launch trigger stopped reproducing): the 338-B blob = constant header `01 08 4b2c91481d9b7da0` ‖ [10:266] RSA-2048-OAEP-SHA1(step-1 cert pubkey, **pearKey16 ‖ hmacKey20**; pearKey16 = the client's FIRST RNG16 draw — byte-equal to the `init_key` input — hmacKey20 the second material) ‖ [266:282] a third fresh RNG16 ‖ [282:286] `u32be(32)` (the serializer's BE length marker for the next field) ‖ [286:318] **field32 = mapA[encrypt_cbc(plain32, iv16, init_key(pearKey16))]** where mapA is a 256-B byte→byte substitution table at .so 0x2249f9 (the post-encrypt loop is `table[byte]`, NOT xor) and `plain32 = mapB[02 ‖ u32be(1) ‖ innerKey16 ‖ zeros(10)]` with mapB the substitution table at 0x224af9 (S2[0]=0x72 — the '0x72-fill' explained) over the 21-B serializer output `u8 tag=2 ‖ u32be version=1 ‖ innerKey16` zero-padded to 32 (innerKey16 = a second, independent RNG16 — opaque to the server until field32 is decrypted); the encrypt_cbc iv rides an in/out 16-B block (entry = the fresh-RNG iv, return = the last ciphertext block) ‖ [318:338] HMAC-SHA1(hmacKey20, field32) (re-verified). Role model unchanged: possession-of-pearKey16 bound to the blob. Kotlin `registration` `NacRequestBlob` (+ the two tables appended to `PearTablesData`), 213 registration tests green; imessage `ClearNacValidationSource` unstubbed at C56-a. Remaining live-mint gate: C56-c only (session250 HardwareConfig values).
 
 ### 1.2 Activation endpoints and certificates
 
@@ -330,6 +330,7 @@ Ordered by value. IDs match the inline `TODO(capture):` markers above.
 
 
 ## Revision history
+- Rev 35 (2026-10-12, C56-a CLOSED — direct in-process replay of ValidationCtx::new, two byte-verified runs): the request blob's full recipe — header ‖ OAEP(pubkey, pearKey16 ‖ hmacKey20) ‖ RNG16 ‖ u32be(32) ‖ field32 ‖ HMAC-SHA1(hmacKey20, field32), with field32 = mapA[encrypt_cbc(mapB[02 ‖ u32be(1) ‖ innerKey16 ‖ zeros], iv, init_key(pearKey16))] and mapA/mapB the 0x2249f9/0x224af9 byte-substitution tables (table[byte], not xor). Kotlin `NacRequestBlob`; imessage unstubbed at C56-a; live-mint gate = C56-c only.
 
 - Rev 34 (2026-10-09, C56-a request-blob field map ~85% pinned — four instrumented runs): the 338-B request blob decomposes as header ‖ RSA-2048-OAEP-SHA1(cert pubkey, pearKey16 ‖ hmacKey20) ‖ 20 B (unpinned, ends u32be(32)) ‖ 32 B pear-AES field (derivation open) ‖ HMAC-SHA1(hmacKey20, the 32-B field) — the HMAC chain verified byte-exact. Live mint still gated on the two unpinned C56-a sub-fields; C58 parser + §1.2/§1.4 activation chain wired in imessage (`register()`), tool UI inputs (export-code paste, courier push token) pending.
 - Rev 33 (2026-10-09, the sign-model fresh-input divergence CLOSED — the last functional live-mint blocker on the sign path): two session-20-frozen constants inside `SignState::sign` are falsified and replaced by their input-dependent forms — the staging maze's i==10 `ecx2` index (`perm2u[st[0x6fa2]]`, was frozen `perm2u[0x40]`) and the ENTIRE P region state+0x6898 (7×256; five of seven tables are parameterized on five body-derived byte XOR pairs via the SSE builder at 0x17a1381-0x17a20b5 — the "byte-identical across base/mod/body-flip" claim held only because those captures shared a body). The builder stream is serialized into generated Kotlin (`NacPTable`) and re-executed lane-wise, byte-exact vs the emulated builder on fresh + random + s20 states. `NacSign` re-ported with all body-derived regions computed (region6f98/0x6fd8/0x6fe8/0x6fec/N/cursor/RC); fresh live sig16 + full 517-B stamp byte-exact, session-20 still byte-exact; 209 registration tests green, imessage `:server:testDebugUnitTest` green. Live mint still gated on C56-a + C56-c (capture) and C58 (OABS parser).
diff --git a/registration/src/main/kotlin/dev/fenn/imessage/registration/NacRequestBlob.kt b/registration/src/main/kotlin/dev/fenn/imessage/registration/NacRequestBlob.kt
new file mode 100644
index 0000000..39f0c40
--- /dev/null
+++ b/registration/src/main/kotlin/dev/fenn/imessage/registration/NacRequestBlob.kt
@@ -0,0 +1,104 @@
+package dev.fenn.imessage.registration
+
+import java.security.PublicKey
+import java.security.SecureRandom
+import javax.crypto.Cipher
+import javax.crypto.Mac
+import javax.crypto.spec.SecretKeySpec
+
+/**
+ * The §1.1 step-2 `session-info-request` blob (C56-a — the 338-B request the client sends
+ * with the step-1 certificate's public key wrapped inside). Field map pinned 2026-10-12 by
+ * direct in-process replay of `ValidationCtx::new` (two independent runs, byte-verified;
+ * NAC-NOTES.md "Session-24 continuation" + spec §1.1 rev 35):
+ *
+ * ```
+ * blob 338 B = header `01 08 4b2c91481d9b7da0`                                  (10 B, constant)
+ *   ‖ RSA-2048-OAEP-SHA1(step-1 cert pubkey, pearKey16 ‖ hmacKey20)             (256 B)
+ *   ‖ slot16 (16 fresh client RNG bytes)                                        (16 B)
+ *   ‖ u32be(32) — the next field's length marker                                (4 B)
+ *   ‖ field32 = blobFieldMap[PearAes.encryptCbc(plain32, iv16, PearAes.initKey(pearKey16))]
+ *                                                                               (32 B)
+ *   ‖ HMAC-SHA1(hmacKey20, field32)                                             (20 B)
+ * ```
+ *
+ * `plain32 = blobPayloadMap[02 ‖ u32be(1) ‖ innerKey16 ‖ zeros(10)]` — the wire format the
+ * binary's serializer writes (`u8 tag=2, u32be version=1, key16`), zero-padded to the 32-B
+ * pear-AES block pair and then byte-mapped through the payload table. `blobFieldMap` /
+ * `blobPayloadMap` are the .so's byte→byte substitution tables at 0x2249f9 / 0x224af9 (the
+ * serializer and the post-encrypt loops apply `table[byte]`, not XOR).
+ *
+ * Role model: the server decrypts the OAEP → (pearKey16, hmacKey20), derives the PAESKey
+ * from pearKey16, decrypts field32, and verifies the HMAC — a possession-of-pearKey16 proof
+ * bound to the blob. Everything is minted locally: three fresh RNG draws plus the caller's
+ * pearKey16 (the SAME pearKey16 the §1.1 key establishment consumes — [NacMint.keyEstablishmentFull]).
+ */
+object NacRequestBlob {
+
+    /** The constant 10-byte header every observed blob starts with. */
+    val header: ByteArray = byteArrayOf(
+        0x01.toByte(), 0x08, 0x4b.toByte(), 0x2c.toByte(), (0x91).toByte(),
+        0x48, 0x1d.toByte(), (0x9b).toByte(), 0x7d.toByte(), (0xa0).toByte(),
+    )
+
+    const val BLOB_BYTES = 338
+    const val PEAR_KEY16_BYTES = 16
+
+    /** Builds the blob; [pearKey16] is returned-consumed by the §1.1 key establishment. */
+    fun build(certDer: ByteArray, pearKey16: ByteArray, random: SecureRandom): ByteArray {
+        val certificate = java.security.cert.CertificateFactory.getInstance("X.509")
+            .generateCertificate(certDer.inputStream())
+        return build(certificate.publicKey, pearKey16, random)
+    }
+
+    fun build(publicKey: PublicKey, pearKey16: ByteArray, random: SecureRandom): ByteArray =
+        build(publicKey, pearKey16) { n -> ByteArray(n).also(random::nextBytes) }
+
+    /** Deterministic core (tests): every randomness draw routes through [draw]. */
+    internal fun build(publicKey: PublicKey, pearKey16: ByteArray, draw: (Int) -> ByteArray): ByteArray {
+        require(pearKey16.size == PEAR_KEY16_BYTES) {
+            "pearKey16 must be $PEAR_KEY16_BYTES bytes (got ${pearKey16.size})"
+        }
+        val hmacKey20 = draw(20)
+        val innerKey16 = draw(16)
+        val slot16 = draw(16)
+        val iv16 = draw(16)
+
+        val paesKey = PearAes.initKey(pearKey16)
+        val plain32 = ByteArray(32)
+        plain32[0] = 0x02
+        plain32[4] = 0x01 // u32be(1) — the serializer's version field
+        innerKey16.copyInto(plain32, W16_OFFSET)
+        val payloadMap = PearTables.blobPayloadMap
+        val mappedPlain = ByteArray(32) { i -> payloadMap[plain32[i].toInt() and 0xff] }
+        val enc32 = PearAes.encryptCbc(mappedPlain, iv16, paesKey)
+        val fieldMap = PearTables.blobFieldMap
+        val field32 = ByteArray(32) { i -> fieldMap[enc32[i].toInt() and 0xff] }
+
+        val oaep = Cipher.getInstance(OAEP_TRANSFORMATION).apply {
+            init(Cipher.ENCRYPT_MODE, publicKey)
+        }
+        val oaepOut = oaep.doFinal(pearKey16 + hmacKey20)
+        check(oaepOut.size == 256) { "OAEP output ${oaepOut.size} B, expected 256" }
+
+        val mac = Mac.getInstance("HmacSHA1").apply {
+            init(SecretKeySpec(hmacKey20, "HmacSHA1"))
+        }
+        val tail = mac.doFinal(field32)
+
+        val blob = ByteArray(BLOB_BYTES)
+        header.copyInto(blob, 0)
+        oaepOut.copyInto(blob, 10)
+        slot16.copyInto(blob, 266)
+        blob[282] = 0x00
+        blob[283] = 0x00
+        blob[284] = 0x00
+        blob[285] = 0x20 // u32be(32) — the field32 length marker
+        field32.copyInto(blob, 286)
+        tail.copyInto(blob, 318)
+        return blob
+    }
+
+    private const val W16_OFFSET = 5
+    private const val OAEP_TRANSFORMATION = "RSA/ECB/OAEPWithSHA-1AndMGF1Padding"
+}
diff --git a/registration/src/main/kotlin/dev/fenn/imessage/registration/PearTables.kt b/registration/src/main/kotlin/dev/fenn/imessage/registration/PearTables.kt
index 71d1a6e..23e9c08 100644
--- a/registration/src/main/kotlin/dev/fenn/imessage/registration/PearTables.kt
+++ b/registration/src/main/kotlin/dev/fenn/imessage/registration/PearTables.kt
@@ -57,8 +57,7 @@ internal object PearTables {
     val tc: IntArray by lazy { wordsAt(8464, 256) }
     /** .rodata 0x2465b8 — encrypt T-table D. */
     val td: IntArray by lazy { wordsAt(9488, 256) }
-    /** .rodata 0x2469b8 — establish_key schedule sbox. */
-    val s3: ByteArray by lazy { bytesAt(10512, 256) }
+    /** .rodata 0x2469b8 — establish_key schedule sbox. */    val s3: ByteArray by lazy { bytesAt(10512, 256) }
     /** .rodata 0x246ab8 — establish_key schedule rcon (only bytes 1..10 consumed; the tail overlaps the est-transform tables). */
     val r3: ByteArray by lazy { bytesAt(10768, 256) }
     /** .rodata 0x246ac4 — establish_key transform T-table 0. */
@@ -73,4 +72,8 @@ internal object PearTables {
     val s2: ByteArray by lazy { bytesAt(15120, 256) }
     /** .rodata 0x247bc4 — init_key schedule rcon (only bytes 1..10 consumed). */
     val r2: ByteArray by lazy { bytesAt(15376, 256) }
+    /** .rodata 0x2249f9 — the §1.1 request blob's pear-AES-output byte map (table[byte]). */
+    val blobFieldMap: ByteArray by lazy { bytesAt(15632, 256) }
+    /** .rodata 0x224af9 — the §1.1 request blob's plaintext byte map (table[byte]). */
+    val blobPayloadMap: ByteArray by lazy { bytesAt(15888, 256) }
 }
diff --git a/registration/src/main/kotlin/dev/fenn/imessage/registration/PearTablesData.kt b/registration/src/main/kotlin/dev/fenn/imessage/registration/PearTablesData.kt
index bb5ae77..c1235fd 100644
--- a/registration/src/main/kotlin/dev/fenn/imessage/registration/PearTablesData.kt
+++ b/registration/src/main/kotlin/dev/fenn/imessage/registration/PearTablesData.kt
@@ -1,22 +1,24 @@
 package dev.fenn.imessage.registration
 
 /**
- * GENERATED FILE — regenerate with the extraction script described in WORKLOG (session: NAC/pear
- * port); do not hand-edit. The pear_aes / NAC white-box .rodata tables (librust_lib_bluebubbles),
- * embedded as base64 source so no Apple-derived binary ships in the repo: one 15632-byte image
- * of the 26 tables consumed by [PearTables], concatenated in vaddr order
- * (0x1a0ea0 .. 0x247cc4; the r3 tail deliberately overlaps the est-transform tables — the key
- * schedule only consumes rcon bytes 1..10). [PearTables] decodes it once at first use; raw dev
- * copies stay under registration/dev/clearadi/ (gitignored) for byte-level cross-checks.
+ * GENERATED FILE — the pear_aes / NAC white-box .rodata tables (librust_lib_bluebubbles),
+ * embedded as base64 source so no Apple-derived binary ships in the repo: one 16144-byte image
+ * of the 28 tables consumed by [PearTables], concatenated in vaddr order (0x1a0ea0 .. 0x247cc4,
+ * then the two 2026-10-12 request-blob byte maps 0x2249f9/0x224af9 appended — the original
+ * extraction script's vaddr ordering was not re-run, the maps are tail-appended). [PearTables]
+ * decodes it once at first use; raw dev copies stay under registration/dev/clearadi/ (gitignored)
+ * for byte-level cross-checks.
  */
 internal object PearTablesData {
-    /** pear tables image, base64, 6 chunk(s) — concatenate in order. */
+    /** pear tables image, base64, 8 chunk(s) — concatenate in order. */
     val pearChunks: List<String> = listOf(
-        "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",
-        "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",
-        "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",
-        "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",
-        "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",
-        "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",
+        "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",
+        "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",
+        "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",
+        "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",
+        "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",
+        "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",
+        "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",
+        "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",
     )
 }
diff --git a/registration/src/test/kotlin/dev/fenn/imessage/registration/NacRequestBlobTest.kt b/registration/src/test/kotlin/dev/fenn/imessage/registration/NacRequestBlobTest.kt
new file mode 100644
index 0000000..286ff40
--- /dev/null
+++ b/registration/src/test/kotlin/dev/fenn/imessage/registration/NacRequestBlobTest.kt
@@ -0,0 +1,102 @@
+package dev.fenn.imessage.registration
+
+import java.security.KeyPairGenerator
+import java.security.SecureRandom
+import javax.crypto.Mac
+import javax.crypto.spec.SecretKeySpec
+import kotlin.test.Test
+import kotlin.test.assertContentEquals
+import kotlin.test.assertEquals
+import kotlin.test.assertFailsWith
+import kotlin.test.assertTrue
+
+/** Synthetic-vector tests for the §1.1 step-2 request blob (C56-a; spec §1.1 rev 35). */
+class NacRequestBlobTest {
+
+    private class FixedDraw(values: List<ByteArray>) {
+        val drawn = mutableListOf<ByteArray>()
+        private val queue = ArrayDeque(values)
+        fun next(n: Int): ByteArray {
+            val v = queue.removeFirst()
+            assertEquals(n, v.size, "draw size")
+            drawn.add(v)
+            return v
+        }
+    }
+
+    private fun keyPair() = KeyPairGenerator.getInstance("RSA").apply { initialize(2048) }.generateKeyPair()
+
+    private fun blob(publicKey: java.security.PublicKey, draw: FixedDraw): Pair<ByteArray, ByteArray> {
+        val pearKey16 = ByteArray(16) { (it * 17 + 3).toByte() }
+        val out = NacRequestBlob.build(publicKey, pearKey16) { n -> draw.next(n) }
+        return out to pearKey16
+    }
+
+    @Test
+    fun blobShape() {
+        val pair = keyPair()
+        val draw = FixedDraw(
+            listOf(
+                ByteArray(20) { it.toByte() },   // hmacKey20
+                ByteArray(16) { (it + 1).toByte() }, // innerKey16
+                ByteArray(16) { (it + 2).toByte() }, // slot16
+                ByteArray(16) { (it + 3).toByte() }, // iv16
+            ),
+        )
+        val (blob, pearKey16) = blob(pair.public, draw)
+        assertEquals(NacRequestBlob.BLOB_BYTES, blob.size)
+        assertContentEquals(NacRequestBlob.header, blob.copyOfRange(0, 10))
+        // slot16 rides at [266:282], followed by the u32be(32) length marker
+        assertContentEquals(draw.drawn[2], blob.copyOfRange(266, 282))
+        assertContentEquals(byteArrayOf(0, 0, 0, 0x20), blob.copyOfRange(282, 286))
+        // OAEP decrypt round-trip: the plaintext is pearKey16 ‖ hmacKey20
+        val cipher = javax.crypto.Cipher.getInstance("RSA/ECB/OAEPWithSHA-1AndMGF1Padding")
+        cipher.init(javax.crypto.Cipher.DECRYPT_MODE, pair.private)
+        val plain = cipher.doFinal(blob.copyOfRange(10, 266))
+        assertEquals(36, plain.size)
+        assertContentEquals(pearKey16, plain.copyOfRange(0, 16))
+        assertContentEquals(draw.drawn[0], plain.copyOfRange(16, 36))
+        // the tail is HMAC-SHA1(hmacKey20, field32)
+        val mac = Mac.getInstance("HmacSHA1")
+        mac.init(SecretKeySpec(draw.drawn[0], "HmacSHA1"))
+        assertContentEquals(mac.doFinal(blob.copyOfRange(286, 318)), blob.copyOfRange(318, 338))
+    }
+
+    @Test
+    fun field32IsMappedEncryptedPayload() {
+        val hmacKey20 = ByteArray(20) { (0x40 + it).toByte() }
+        val innerKey16 = ByteArray(16) { (0x50 + it).toByte() }
+        val slot16 = ByteArray(16) { (0x60 + it).toByte() }
+        val iv16 = ByteArray(16) { (0x70 + it).toByte() }
+        val draw = FixedDraw(listOf(hmacKey20, innerKey16, slot16, iv16))
+        val (blob, pearKey16) = blob(keyPair().public, draw)
+
+        val plain32 = ByteArray(32)
+        plain32[0] = 0x02
+        plain32[4] = 0x01
+        innerKey16.copyInto(plain32, 5)
+        val mappedPlain = ByteArray(32) { i -> PearTables.blobPayloadMap[plain32[i].toInt() and 0xff] }
+        val enc32 = PearAes.encryptCbc(mappedPlain, iv16, PearAes.initKey(pearKey16))
+        val field32 = ByteArray(32) { i -> PearTables.blobFieldMap[enc32[i].toInt() and 0xff] }
+        assertContentEquals(field32, blob.copyOfRange(286, 318))
+    }
+
+    @Test
+    fun rejectsWrongPearKeySize() {
+        val draw = FixedDraw(listOf(ByteArray(20), ByteArray(16), ByteArray(16), ByteArray(16)))
+        assertFailsWith<IllegalArgumentException> {
+            NacRequestBlob.build(keyPair().public, ByteArray(15)) { n -> draw.next(n) }
+        }
+    }
+
+    @Test
+    fun publicBuildIsRandomizedAndWellFormed() {
+        val pearKey16 = ByteArray(16).also(SecureRandom()::nextBytes)
+        val blob = NacRequestBlob.build(keyPair().public, pearKey16, SecureRandom())
+        assertEquals(NacRequestBlob.BLOB_BYTES, blob.size)
+        assertContentEquals(NacRequestBlob.header, blob.copyOfRange(0, 10))
+        val blob2 = NacRequestBlob.build(keyPair().public, pearKey16, SecureRandom())
+        // fresh randomness per build: the OAEP ciphertext (padded RSA) must differ
+        assertTrue(!blob.contentEquals(blob2))
+    }
+}