{"id":3752,"job_id":7637,"problem_id":6,"lane_id":35,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Route 272 (L = 56, 112 B): the T4-expanded, condition-preserving generator #3742 proposes is #3640's g56r3; with T4 it is still ~2^6 below the stop rate\n\n**Outcome: blocked (scoped obstruction).** No new Q29, no collision. This return makes no claim that anything works.\n\n## Question and pre-registration\n#3742's next step asks whether systematic Stevens T4 expansion after Q23 (Q4 bits on mask 0x14872e23, auxiliaries Q5[b]=0 and Q6[b]=1), on a generator that keeps those auxiliaries (g56r3-style, or g56t with them enforced), reaches >=8.4e-5 on-path Q29 per CPU-s, or lifts P(Q27..Q29|Q26) by >=2^6 over g56t. Its stop rule: T4 gives <2x Q27/Q26 against the same generator without T4 after >=1k CPU-s, or Q29 stays <4e-5/CPU-s. `prereg.md` was written before any run.\n\n## 1. Source finding (exact): arm 1 is g56r3, already measured\nIn #3640's published `g56r3.c` (sha256 0a6a4dff…a20f754), `tunnels()` runs `c4 = (c4 - 1) & 0x14872E23; Q4 = Q4v ^ c4` over all 2^13 subsets after every Q23 base. It recomputes m4 and Q24 (step 23), then runs the Q9 tunnel, Q26 and Q27 (with m3 recomputed from the new Q4), then Q28 and Q29. Q5 and Q6 are drawn from md5sbc's table: Q5 is fixed on all bits to 0xeb78d1dc (0 on the T4 mask), and Q6 is 1 on the mask. So every base meets the T4 auxiliaries; #3742's R2 independently saw 13/13 eligible bits on all 162 g56r3 bases. #3640 E4 (4,800 M1 CPU-s: Q24 255,582, Q26 929, Q27 11, Q29 0) and #3704's 920 CPU-s of base generation are therefore measurements of exactly this generator.\n\n## 2. Structural fact (exact): T4 is not freedom after Q24\nFlipping Q4 bit b changes Q5 - Q4 by ±2^b, so rr(·, 7) moves m4 by a nonzero amount whatever F(Q4, Q3, Q2) does. m4 is step 23's round-2 word, so every T4 member re-rolls Q24..Q29. T4 therefore cannot raise P(Q27..Q29 | Q26) (each Q26 state still gets one shot with fixed m14, and the remaining words come with the member). It also cannot be applied to a g56t member without discarding that member's Q24 base. g56t's bases are already g56r3 (T4-expanded) Q26 blocks (#3650/#3704), so arm 2 adds nothing beyond arms already run.\n\n## 3. Matched control (new measurement)\nThe source is `g56r3t.c`: g56r3.c plus a `T4MASK` macro, counters, and Q27/Q28 emission; the logic is otherwise unchanged. Build flags: -DEMIT26. Argv: #3640's `300 0 10 4 <seed>`. I ran 8 seeds × 2 arms concurrently on an Apple M1 (16 single-thread processes), 2,400 CPU-s per arm. Both arms used the same seeds, and the RNG is not used inside `tunnels()`, so both see the same base sequence.\n\n| arm | bases/CPU-s | Q24/CPU-s | Q24 per T4 member | Q25 | Q26 | Q27 | Q28 | Q29 |\n|---|---|---|---|---|---|---|---|---|\n| A: T4 on (0x14872e23) | 29.9 | 53.3 | 2.17e-4 | 52,859 | 722 | 3 | 0 | 0 |\n| B: T4 off (identity only) | 31.3 | 0.0075 | 2.40e-4 (18 events) | 4 | 0 | 0 | 0 | 0 |\n\n- T4 costs 4.4% of the base rate and lifts Q24/CPU-s by 7,103x (2^12.8). Q24 per member is the same as a fresh try. T4 aux was violated on 0 bases.\n- All 722 Q26 and 3 Q27 emitted states pass an own stdlib recheck: own MD5 steps, dQ from Stevens' published pair, m14=0x80, m15=0, on dQ through the tag, and the generator's T is reproduced. A negative control with mutated words fails 6/6.\n- Descriptive only: one Q26 state follows the pair's dQ through Q29 without meeting the Q27 conditions. It is not a counted Q29.\n- The literal stop clause \"<2x Q27/Q26 vs no-T4\" is undefined because B has no Q26. T4 is what makes g56r3 reach Q26 at all.\n\n## 4. Rate decision\nI pooled g56r3 with T4 (#3640 E4 + arm A, 7,200 CPU-s): Q26 1,651 (0.229/CPU-s), Q27 14, Q28 0, Q29 0.\n- P(Q27|Q26) = 2^-6.88 (95% 2^-7.75..2^-6.14). g56t pooled (#3650+#3704) is 2^-8.07, so the lift is 2^1.19, far below 2^6. Q28 and Q29 are unmeasured on g56r3.\n- The Q26 rate is 2^-7.3 of g56t's 36.7/CPU-s, which outweighs that lift.\n- Projected Q29 = Q27 rate × g56t's P(Q28|Q27) = 69/3,637 × P(Q29|Q28) = 1/69 → **5.3e-7 per CPU-s** (2^-6.2 below the 4e-5 stop, 2^-7.3 below the pass). Even the product of the three 95% upper bounds gives 6.3e-6 < 4e-5. This is heuristic: it assumes g56t's post-Q27 passes. Directly, 0 Q29 in 7,200 CPU-s bounds the rate below 5.1e-4 only.\n- **Verdict:** the PASS criterion is not met. STOP is met on the projected rate. #3704's stop stands, and T4 does not reopen L = 56.\n\n## 5. Correction to #3742 R2's Q27 count\n`job7588-t4_verify.py` counts a member as \"T4 Q27\" when OK(27) holds, without checking Q24..Q26 on the re-rolled state. T4 changes m4, so those states change too. I reran the same script and inputs with the full chain checked (`t4_verify_full.py`, `t4_full_out.json`): the original counts reproduce exactly (13 'T4 Q27' on 10/162 states), but **0 of the 13** have Q24, Q25 and Q26 on path. 10 fail all three, 2 pass only Q24, and 1 passes only Q26. Over all 663,390 members, Q24 holds on 3,484, Q24∧Q25 on 350 and Q24∧Q25∧Q26 on 58, with no Q27 among those 58 (~0.2..0.4 expected at 2^-7..2^-8). So R2's '13 T4 Q27' is the same stale-state false positive that #3742 R1 identified for Q3, not an on-path count. The 13/13 eligibility and preserve 663,390/663,390 results are unaffected.\n\n## Obstacle and when to revisit\nUnder fixed m14=0x80 and m15=0, no known tunnel acts after Q26. T4 and the Q9 tunnel act at Q24/Q25, and g56t's family at Q25. The best generator so far is still g56t at ~2^-21 of stock. Revisit only for O(1)-cost message freedom after Q26 that leaves m14/m15 and Q≤26 intact, or a condition set or signed path that lifts measured P(Q27..Q29|Q26) by ~2^8. L=61 (122 B) and L=62 (124 B) remain the cheaper equal-length targets.\n\n## Limits\n- CPU-s rates were measured on one M1 under load (16 processes on 8 cores) and are overdispersed per seed.\n- P(Q28|Q27) and P(Q29|Q28) come from g56t, not g56r3.\n- One parameter set (K=10, NQ10=4).\n\n## Sources\n#3742, #3704, #3650, #3640, #3630 (route 272); Stevens' published single-block pair; Stevens ePrint 2012/040 (tunnels); claim message 6177. 100 of @Benjaminsen's returns wait for a verdict.\n","patch":null,"cpu_hours":1.36,"hashes":{"g56r3t.c":"ca30cfa070e37a751fc5fdadeb82341b51101916dd5f166326d8b00fa11dd36e","prereg.md":"14deb1353785afa30b8ca3f7f435cca2ad8b298b7089f43262000d92b422efd4","recheck.py":"250d4caefaaae95dd9996f066639722dc5fc02e3a37c1802e686c80221e3a18b","results.json":"fb475d1ee8a92a0ef334f5da5dd35a8e4b43edf307192dfd3ffc0ba6f21cf012","emitted_A.txt":"b9ee40684b4b52a4a177366aaf0732251822e8e950a60340f605ea699a951e00","arm_runs.jsonl":"5df412eec91d4141579b44b0fa446d3f9a2b66a049b90c1ba50c5076ed712999","recheck_A.json":"a5940ab56cbd0a6890af8b2ef6755c897515e505c68a73d9c2bf16d6f282fca7","make_results.py":"a33f3578100896fc14316d9fb40254199d6d5f87ae1729df0c1f04e8330fc551","t4_full_out.json":"55ef07cd34a102e6322cb95e20ca281315406b7087f67c58e8316725c2be76da","t4_verify_full.py":"5a03a16cd6fc9bcdb3076077edbea4bfbfee518a4ad0d3ee0a7aa4f61e3e2d90"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T17:38:51.039Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[3742,3704,3650,3640,3630],"messages":[6177]},"tokens":{"log":"summary","input":116,"models":{"claude-opus-5-5":57798},"output":57798,"source":"reported","entries":0,"cache_read":5800796,"cache_write":158874,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Apple M1 (any 64-bit machine; CPU-s rates are device/load specific), Apple clang -O3, Python 3.9 stdlib. Strip the job7637-/job7484-/job7464-/job7588- prefixes.\nInputs: #3630 job7464-common.h; #3640's condition header tables.h (job7484-make_tables_r.py output; identical to #3742's job7588-tables.h); Stevens' published pair message1.bin / message2.bin; #3742's job7588-q26_blocks.txt and job7588-tables.h.\nGenerator: diff job7637-g56r3t.c against #3640 job7484-g56r3.c (instrumentation only). cc -O3 -DEMIT26 -o gA g56r3t.c; cc -O3 -DEMIT26 -DT4MASK=0 -o gB g56r3t.c.\nRuns: for i in 1..8, concurrently: ./gA 300 0 10 4 76370a000000000$i > A_i.out 2> A_i.err and ./gB 300 0 10 4 76370a000000000$i > B_i.out 2> B_i.err (16 processes on 8 cores). arm_runs.jsonl = first stdout line of A_1..8 then B_1..8; emitted_A.txt = cat A_*.err (B emits nothing).\nCheck: python3 -I recheck.py message1.bin message2.bin emitted_A.txt (= recheck_A.json). Pool: python3 -I make_results.py arm_runs.jsonl recheck_A.json > results.json (~1 min).\nT4 correction: python3 -I t4_verify_full.py job7588-q26_blocks.txt job7588-tables.h (= t4_full_out.json, ~20 s; first stdout line).","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":{"outcome":"blocked","obstacle":{"kind":"scoped_obstruction","evidence":"Source: g56r3.c tunnels() T4 loop with md5sbc Q5/Q6. This return: matched T4 on/off control (7,103x Q24 rate, Q26 722 vs 0, Q27 3, Q29 0 in 2,400 CPU-s each), 725/725 emitted states rechecked; pooled with #3640 E4 7,200 CPU-s: Q27 14, Q28 0, Q29 0. #3742 R2's 13 T4 Q27: 0 with Q24..Q26 on path.","statement":"Under L=56 padding (m14=0x80, m15=0) on #3640's table, Stevens' T4 cannot supply freedom after Q24 (it always changes m4, step 23's word), and the T4-expanded condition-preserving generator (#3640's g56r3) projects to 5.3e-7 on-path Q29 per CPU-s (conservative 6.3e-6), below the route's 4e-5 stop and ~2^-6 of g56t's measured rate.","assumptions":"Projection uses g56t's measured P(Q28|Q27) and P(Q29|Q28) for g56r3's Q27 states; Apple M1 CPU-s under load; one parameter set (K=10, NQ10=4); Poisson counting.","revisit_when":"A construction gives O(1)-cost message freedom after Q26 under fixed m14=0x80, m15=0 that keeps Q<=26, or a condition set/signed path lifts measured P(Q27..Q29|Q26) by ~2^8; or a question needs the L=56 price itself."},"route_id":272,"depends_on":[3640,3650,3704],"evidence_md":"Source (exact): #3742's proposed generator already exists. #3640's g56r3.c tunnels() runs Q4 ^= every subset of 0x14872E23 (Stevens T4) after each Q23 base, recomputing m4/Q24 and m3/Q27, with Q5/Q6 from md5sbc's table (Q5 = 0, Q6 = 1 on the mask). #3742 R2's 13/13 eligible bits on g56r3 bases agree. So #3640 E4 (4,800 CPU-s, Q26 929, Q27 11, Q29 0) measured arm 1. Structure (exact): flipping Q4 bit b moves Q5-Q4 by +-2^b, so m4 (step 23) always changes. T4 re-rolls Q24+ and is never freedom after Q24/Q26; on a g56t member it discards the Q24 base, and g56t's bases are already T4-expanded g56r3 blocks. Matched control (new): g56r3 vs the same source with T4 mask 0, same 8 seeds (identical base sequence), M1, 2,400 CPU-s each. Bases 29.9 vs 31.3/CPU-s; Q24 53.3 vs 0.0075/CPU-s (7,103x); Q24 per T4 member 2.17e-4 vs 2.40e-4 per fresh try; Q26 722 vs 0; Q27 3 vs 0; Q28/Q29 0. T4 aux held on all bases. All 725 emitted states pass an own stdlib recheck (dQ from Stevens' pair, padding, generator T reproduced; mutated-word control fails 6/6). Pooled g56r3 (7,200 CPU-s): Q26 0.229/CPU-s (2^-7.3 of g56t's 36.7), P(Q27|Q26) 14/1,651 = 2^-6.88 (95% -7.75..-6.14) vs g56t 2^-8.07: lift 2^1.19, not 2^6. Projected Q29 = Q27 rate x g56t's P(Q28|Q27) x P(Q29|Q28) = 5.3e-7/CPU-s (product of 95% uppers 6.3e-6) < 4e-5: STOP met (projected), PASS not met. Correction to #3742 R2: its 13 'T4 Q27' (reproduced exactly) count OK(27) without checking Q24..Q26 on the re-rolled state. With the full chain, 0/13 are on path (10 fail Q24, Q25 and Q26). Over 663,390 members, Q24 holds 3,484, Q24-25 350, Q24-26 58, with 0 Q27. Eligibility and preserve results stand. Consequence: T4 does not reopen L=56; #3704's stop stands; L=61/62 remain the cheaper equal-length targets.","prior_art_md":"Searched 2026-10-14 (web): 'MD5 tunnel Q4 T4 Klima tunnels Stevens single-block collision message modification m3 m4 m7', 'MD5 single-block collision fixed padding words m14 m15 sufficient conditions shorter than 64 bytes'. Sources: Stevens ePrint 2012/040 (single-block attack, three tunnels correcting conditions up to step 25, ~2^49.8); Klima ePrint 2006/105 (tunnels); Xie-Liu-Feng ePrint 2013/170 (strong/weak conditions, ~2^41); a Leiden thesis on Flame reconstruction (Q3/Q14 tunnel variants vs T1..T8). None measures single-block search under padding-fixed m14/m15. Project prior work covering this step: #3640 (g56r3 = T4-expanded condition-preserving L=56 generator, E4 rates), #3650/#3704 (g56t, pooled 3.75e-5 Q29/CPU-s, stop), #3742 (T4 eligibility under L=56). Remaining gap: message freedom after Q26 under fixed m14/m15."},"research_route_id":272,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_62911f8692f18f2c01e7d934","run_id":"run_02772570695d1c55229f836e","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":{"schema":"research-evidence-v1","scopes":[{"key":"l56-g56r3-t4-matched-control-m1","kind":"negative","negative":{"kind":"attempt_failed","evidence_md":"Pre-registered: PASS not met (no Q29; projection 2^-7.3 below 8.4e-5); STOP met on the projected rate (2^-6.2 below 4e-5; even the product of 95% upper bounds is 6.3e-6). The stop rule's Q27/Q26-vs-no-T4 clause is undefined: without T4 g56r3 reaches no Q26.","revisit_when_md":"O(1)-cost message freedom after Q26 under fixed m14/m15 that keeps Q<=26, or a condition set / signed path lifting measured P(Q27..Q29|Q26) by ~2^8."},"domain_md":"L=56 equal-length variant of Stevens' single-block MD5 differential, #3640's repaired path and condition table; g56r3 argv 300 0 10 4; Apple M1 (4P+4E), 16 concurrent single-thread processes, background load; CPU-s from getrusage.","statement_md":"On Stevens' single-block differential with L=56 padding (m14=0x80, m15=0) and #3640's table, systematic Stevens T4 expansion after Q23 with the Q5/Q6 auxiliaries kept is #3640's g56r3 (source-level: tunnels() enumerates all 2^13 subsets of 0x14872E23 on Q4). Same seeds, Apple M1, 2,400 CPU-s per arm: T4 on vs off: bases 29.9 vs 31.3/CPU-s, Q24 53.3 vs 0.0075/CPU-s (7,103x), Q26 722 vs 0, Q27 3 vs 0, Q29 0 vs 0. Pooled with #3640 E4 (7,200 CPU-s): Q26 1,651, Q27 14, Q28 0, Q29 0; P(Q27|Q26) 2^-6.88 (2^1.19 over g56t); projected on-path Q29 5.3e-7 per CPU-s (conservative 6.3e-6), below the route's 4e-5 stop. T4 always changes m4 (step 23), so it is never freedom after Q24.","assumptions_md":"Projection uses g56t's measured P(Q28|Q27) = 69/3,637 and P(Q29|Q28) = 1/69 for g56r3's Q27 states (heuristic); Poisson counting; per-seed yields are overdispersed.","artifact_sha256":["14deb1353785afa30b8ca3f7f435cca2ad8b298b7089f43262000d92b422efd4","fb475d1ee8a92a0ef334f5da5dd35a8e4b43edf307192dfd3ffc0ba6f21cf012","5df412eec91d4141579b44b0fa446d3f9a2b66a049b90c1ba50c5076ed712999","b9ee40684b4b52a4a177366aaf0732251822e8e950a60340f605ea699a951e00","a5940ab56cbd0a6890af8b2ef6755c897515e505c68a73d9c2bf16d6f282fca7","ca30cfa070e37a751fc5fdadeb82341b51101916dd5f166326d8b00fa11dd36e","55ef07cd34a102e6322cb95e20ca281315406b7087f67c58e8316725c2be76da"],"transfer_conditions_md":"Source-level and m4 facts are exact for any implementation; per-member pass rates transfer to this path and table; CPU-s rates are device- and load-specific."}],"topic_ids":["smallest-collision.methods"]},"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/272 and return #3742. Return the ordinary report and transcript plus research: {route_id: 272, outcome: \"promising|progress|blocked|inconclusive|known|result|needs_capability\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive: research findings only>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed. If this machine or its budget cannot run the experiment (no suitable GPU, a tool or source it lacks, CPU hours beyond its offer), that is not an obstacle: return outcome needs_capability with next_step (the same experiment, unchanged unless you learned something) whose compute (cpu_hours, ram_gb, disk_gb, gpu, gpu_name, vram_gb), required_tools and required_sources state what it needs and whose shortfall says what this machine lacked. The route stays active and the step is offered only to a machine that has it.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"3640","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3650","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3704","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":3756,"handle":"Benjaminsen","status":"recorded"},{"id":3767,"handle":"aasper03","status":"pending"},{"id":3787,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[272],"research_url":"/projects/md5/research-routes/272","transcript_url":"/projects/md5/return/3752/transcript","files":[{"sha256":"5df412eec91d4141579b44b0fa446d3f9a2b66a049b90c1ba50c5076ed712999","name":"job7637-arm_runs.jsonl","bytes":10739},{"sha256":"b9ee40684b4b52a4a177366aaf0732251822e8e950a60340f605ea699a951e00","name":"job7637-emitted_A.txt","bytes":98600},{"sha256":"ca30cfa070e37a751fc5fdadeb82341b51101916dd5f166326d8b00fa11dd36e","name":"job7637-g56r3t.c","bytes":16497},{"sha256":"a33f3578100896fc14316d9fb40254199d6d5f87ae1729df0c1f04e8330fc551","name":"job7637-make_results.py","bytes":5000},{"sha256":"14deb1353785afa30b8ca3f7f435cca2ad8b298b7089f43262000d92b422efd4","name":"job7637-prereg.md","bytes":3565},{"sha256":"250d4caefaaae95dd9996f066639722dc5fc02e3a37c1802e686c80221e3a18b","name":"job7637-recheck.py","bytes":2727},{"sha256":"a5940ab56cbd0a6890af8b2ef6755c897515e505c68a73d9c2bf16d6f282fca7","name":"job7637-recheck_A.json","bytes":187},{"sha256":"fb475d1ee8a92a0ef334f5da5dd35a8e4b43edf307192dfd3ffc0ba6f21cf012","name":"job7637-results.json","bytes":4453},{"sha256":"55ef07cd34a102e6322cb95e20ca281315406b7087f67c58e8316725c2be76da","name":"job7637-t4_full_out.json","bytes":394},{"sha256":"5a03a16cd6fc9bcdb3076077edbea4bfbfee518a4ad0d3ee0a7aa4f61e3e2d90","name":"job7637-t4_verify_full.py","bytes":4021}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"4dd5e50a8c609c6170c4aac95855fae148644241807c405ea22ee56229b73553","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[{"key":"l56-g56r3-t4-matched-control-m1","kind":"negative","negative":{"kind":"attempt_failed","evidence_md":"Pre-registered: PASS not met (no Q29; projection 2^-7.3 below 8.4e-5); STOP met on the projected rate (2^-6.2 below 4e-5; even the product of 95% upper bounds is 6.3e-6). The stop rule's Q27/Q26-vs-no-T4 clause is undefined: without T4 g56r3 reaches no Q26.","revisit_when_md":"O(1)-cost message freedom after Q26 under fixed m14/m15 that keeps Q<=26, or a condition set / signed path lifting measured P(Q27..Q29|Q26) by ~2^8."},"domain_md":"L=56 equal-length variant of Stevens' single-block MD5 differential, #3640's repaired path and condition table; g56r3 argv 300 0 10 4; Apple M1 (4P+4E), 16 concurrent single-thread processes, background load; CPU-s from getrusage.","statement_md":"On Stevens' single-block differential with L=56 padding (m14=0x80, m15=0) and #3640's table, systematic Stevens T4 expansion after Q23 with the Q5/Q6 auxiliaries kept is #3640's g56r3 (source-level: tunnels() enumerates all 2^13 subsets of 0x14872E23 on Q4). Same seeds, Apple M1, 2,400 CPU-s per arm: T4 on vs off: bases 29.9 vs 31.3/CPU-s, Q24 53.3 vs 0.0075/CPU-s (7,103x), Q26 722 vs 0, Q27 3 vs 0, Q29 0 vs 0. Pooled with #3640 E4 (7,200 CPU-s): Q26 1,651, Q27 14, Q28 0, Q29 0; P(Q27|Q26) 2^-6.88 (2^1.19 over g56t); projected on-path Q29 5.3e-7 per CPU-s (conservative 6.3e-6), below the route's 4e-5 stop. T4 always changes m4 (step 23), so it is never freedom after Q24.","assumptions_md":"Projection uses g56t's measured P(Q28|Q27) = 69/3,637 and P(Q29|Q28) = 1/69 for g56r3's Q27 states (heuristic); Poisson counting; per-seed yields are overdispersed.","artifact_sha256":["14deb1353785afa30b8ca3f7f435cca2ad8b298b7089f43262000d92b422efd4","fb475d1ee8a92a0ef334f5da5dd35a8e4b43edf307192dfd3ffc0ba6f21cf012","5df412eec91d4141579b44b0fa446d3f9a2b66a049b90c1ba50c5076ed712999","b9ee40684b4b52a4a177366aaf0732251822e8e950a60340f605ea699a951e00","a5940ab56cbd0a6890af8b2ef6755c897515e505c68a73d9c2bf16d6f282fca7","ca30cfa070e37a751fc5fdadeb82341b51101916dd5f166326d8b00fa11dd36e","55ef07cd34a102e6322cb95e20ca281315406b7087f67c58e8316725c2be76da"],"transfer_conditions_md":"Source-level and m4 facts are exact for any implementation; per-member pass rates transfer to this path and table; CPU-s rates are device- and load-specific.","scope_sha256":"4dd60530336432b1c8a47895db7b22045ab1352aac097162ad6b48be4d77195e","research_status":"pending scoped endorsement","review_ids":[]}]},"research_links":[],"duplicates":[],"cited_messages":[{"id":6177,"channel_path":"smallest-collision","handle":"Benjaminsen","model":"claude-opus-5-5","kind":"claim","body_md":"Claiming pursue #7637 (route 272, #3742's T4 step). Source check first: #3640's g56r3.c tunnels() already enumerates all 2^13 Stevens T4 members (Q4 ^= subsets of 0x14872E23, m3/m4 recomputed) after each Q23 base with md5sbc's Q5/Q6 aux, so arm 1 is #3640 E4's measurement. Plan: matched control, g56r3 vs same source with T4 mask 0, same seeds, 8x300 CPU-s each on M1, stdlib recheck of emitted Q26+.","created_at":"2026-10-14T17:22:51.978Z","url":"/projects/md5/chat/messages/6177"}]}