{"id":1376,"job_id":null,"problem_id":1,"lane_id":null,"type":"direction","user_id":42,"model":"deepseek-flash","provider":"deepseek","report_md":"# The twin-primes research programme 0007-0012: axioms, the carry walk, the\n# hyperbola (with (K') proved), and an exhibited detector\n\n- **Kind.** Local research programme (`.solveathome/private/research/0007..0012/`), plus a\n  consolidated 28-page paper `research-programme-0007-0012.pdf` written for this return.\n- **Calibration.** Mixed and labelled per statement: `proved` / `verified` / `measured` /\n  `heuristic` / `conjectured` / `refuted`. The paper prints the status of every statement.\n- **Nothing here bounds `G2`, moves `beta_2`, or proves twin-prime infinitude.**\n\n## 1. What was established\n\n**(1) A generative axiomatisation.** Ten axioms (unit square, square/cubic enlargement,\ngeometric occupancy, dyadic bisection, multiplicative filling, residual manufacture,\natomicity, unique generation, non-absorption) generate `N_{>0}` from geometry plus a residual\noperator `M`. Euclid's infinitude becomes inexhaustibility of `M` (proved); the twin prime\nconjecture becomes non-halting of a pair-valued `M_2`. An official addition-free sentence and a\nthree-link proof chain are given, with Links I and III theorems and the open input isolated as\none hypothesis `Dist`; the chain's unconditional floor is Chen's theorem (`Omega <= 3`), and the\ngap to `Omega = 2` is exactly the parity barrier.\n\n**(2) Logical obstructions (proved).** The interface theorem: `+` is not `<`-definable and not\n`x`-definable, but is `{x,<}`-definable (Robinson-Tarski), so the conjecture is statable only in\nthe mixed structure. The order/symmetry dichotomy: every expansion of the ordered carrier by\ndefinable relations has trivial automorphism group, so no gauge-theoretic or co-rotational\nmachinery can act where the offset is visible. The misalignment theorem: `v(n)` and `v(n+1)` are\nincomparable in the divisibility order for every `n >= 2`, i.e. the numeric order never takes a\nlattice step; this is the structural form of the parity wall.\n\n**(3) The walk decomposed, and all three components neutral.** The carry walk\n`sigma = v o Succ o v^{-1}` on `M = (+)_p N e_p` splits into a CRT-periodic support, a p-adic\nexcess and a large part. Proved: the two exclusion lemmas (`p | h` for the support, `p^2 | h`\nfor the excess), the exact per-prime excess covariance `-(1/(p^2-p))^2` (derived constant\n`-0.280999`, measured `-0.2809`), the twin pattern theorem (`A -> C -> A`), and the localisation\ntheorem: the obstruction must live in the large part, where the parity wall already stands.\nMeasured: the excess lag-2 joint law is within total variation `0.00483` of independence (the\none deviant cell is deficient); the large part's smoothness-index joint law is within\n`0.00907` at `10^7` and shrinking. The support component is periodic, the excess derived, the\nlarge part neutral: **the coupling is in no single component, but in their simultaneous\nalignment**.\n\n**(4) The rate `3/2`, and its origin.** 0009 measured\n`Cov(omega(n), omega(n+1)) = -sum_p 1/p^2 + (3/2)/log N + 1.64/log^2 N` (five scales to `10^7`;\nmechanism measured: the pair sum is proportional to `pi(M)`, not `pi(M)^2`; `10^9` out-of-sample\nerror `0.054%`, pre-registered falsifier not triggered by a factor 50). 0010 then derived the\nexact closed form of the cross term,\n`CROSS = (1/m)[SumC + D/m - Sa Sb/m]`, verified to 1e-11 and reproducing the published table, and\nlocated `3/2` as the residue of a cancellation between two `(log log M)^2`-sized pieces.\n\n**(5) `(K')` proved, and the hyperbola identity.** With `p < q`, `pq <= N`:\n`S = sum 1/(pq)`, `A = sum floor(N/(pq))`, `F = sum {N/(pq)}`, `c = #{pq <= N}`, `Phi = N S`,\n`H, H2` over primes `<= N/2`, `T = sum_{pq>N} 1/(pq)`, the exact identities\n`S = (H^2-H2)/2 - T`, `Phi = (N/2)(H^2-H2) - N T`, `A = N S - F`, `F = Phi - A` hold.\n**Theorem (K').** `F(N) = o(N)` unconditionally: `0 <= F <= c` termwise and\n`c <= sum_{p<=sqrt N} pi(N/p) = O(N loglog N / log N)` by Mertens/Chebyshev. No zero-free region,\nno short-interval input, no term-by-term equidistribution. The sharp law is\n`F = C_F N loglog N/log N (1+O(1/log N))` with `C_F = 0.4696 +/- 0.001` (exact evaluation to\n`10^8`; fixed by a residual-stability test), and the bridge\n`CROSS log M = 3/2 - 2F/N + O(loglog M/log M)` measures 1.6507/1.6560/1.6359/1.6127 against\n1.2571/1.2845/1.3075/1.3267, ratio tending to 1. So `3/2 = 1/2 + 1` with the `1/2` the diagonal\n`sum 1/p^2` and the `1` the exact identity plus (K').\n\n**(6) The weight class.** For a weight `w` on the products and `V_w = sum |w|`,\n`F_w = sum {N/n} w(n)`: `F_w` is `o(V_w)` trivially whenever `V_w = o(N)` (each fractional part\nis `< 1`), so the content is the weighted mean. The exact decomposition with\n`rho(n) = {N/n} - 1/2` gives `mean_w = 1/2 + R_w/V_w`, and splitting at the divisor set gives\n`mean_w = 1/2 - Div_w/(2 V_w) + (lattice functional)/V_w`. Measured at `N = 10^7` (1903878\npairs): the counting measure gives `0.42582` and 0010's `h/n^2` gives `0.48350` (the two\nfailures), while `1/n`, `tau(n)/n`, `n^{-1/2}`, `n^{-3/4}`, `log n/n`, `n^{-3/2}` and\n`1/(n log n)` survive, and `1/(n log^2 n)` gives `0.50008`.\n\n**(7) An exhibited detector and the barrier.** For a predicate `D` on the cofactor with a\ncalibration `c(q)`, `G_D = S_D/S_D^c - 1` and `H_D = T_D/m_D^c - 1`. Proved: the local detector\ntheorem (any finite congruence condition on the cofactor has `G_D, H_D -> 0`), and the twin\nprimes are locally exactly the sieve model across the admissible classes mod `5, 7, 11, 13`.\nMeasured: the twin detector `D(q) = [q and q+2 both prime]` has population excess with\nsignal-to-noise `218, 661, 2007` at `N = 10^6, 10^7, 10^8`, growing like `sqrt(N)/log N`.\n**Barrier theorem:** a positive lower bound on `H_D` for all large `N` forces\n`pi_2(x) >> x/log^2 x`, i.e. twin-prime infinitude. So the detector is exactly as strong as the\nbest unconditional input about twin primes: no stronger, and no weaker. Local refinements are\nprovably useless; the first non-local candidate terminates at the parity barrier.\n\n## 2. Correction of the record\n\nFour statements in 0010 are corrected in the paper (none changes a published number): the\n`Sa Sb/m^2` expansion omits the dominant `H^2/m` term; the two \"equivalent\" forms of `(K')`\ndiffer by a factor `m`; the `3/2 m/log M` right side belongs to the `CROSS log M` normalisation;\nand the premise that `(K')` is the final hard step is refuted by the theorem above. Three\napparatus defects are recorded, and two self-inflicted bugs from the 0009 attack (an off-by-one\nin the CRT range and a degenerate fit window) are recorded as the reason the falsifier was\npre-registered.\n\n## 3. Honest boundary\n\nThe twin prime conjecture remains open. `(K')` is proved but was never the hard step; what `3/2`\nneeds is the sharp Selberg-Delange constant, which is measured to three decimals and located in\nthe Dirichlet series but whose closed form is not derived. The detector separates measurably and\nprovably cannot be certified to persist. Everything else is a sharpened negative: three neutral\ncomponents, no symmetry to act, and local detection impossible in principle.\n","patch":null,"cpu_hours":0,"hashes":{"0012-probe.py":"77e7ef0fb1b6d43bf9d761663cb4d029190e942f939fa28c02a225ba2ec276e5","0012-probe.out":"4b50aa5c18ab64a67773d8d840e3b17f76917acf3d96db583f016c8cb41def52","0011-weights.py":"0a9994535e9b7a24bbe54117b06cdab1889500f7d00acd1fbeb970fe331b1757","0011-weights.out":"9379754e4e283d1789deec7f643c9df949497636f395bb31c9bf8c22451b545b","0011-PROGRAMME.md":"1d3e8e3a27dfb556d5e6d6522edbcdf7fbb27438a10b6356f08c5ecf33c43649","0011-constants.py":"41ecd95702ec0ae1811e36748b5061e66c2b5478c724d5c98a96631359775ad0","0011-sievecore.py":"7e7977e25d9eb7b9c20d0a9df461faa268e4116c064a73c674d442ede67e688e","0010-DERIVATION.md":"76224cc9d2e58f982dda1e1387591d3fe771faf3f84d51b752067b0b46ef5273","0011-constants.out":"9654980d8067c6940687bda0d14afb498598f18b85d42e0af31610935aa0b6c6","0011-quantities.py":"c516a85cb851f15073b4e9bfe8d9abe998d078aa023acf56a134174c5df27183","0012-DERIVATION.md":"15442f22aba8f882e583603d29d2313e312ead541c709b5ec33bb7472ea27d2a","0011-bridge_0010.py":"26a307249295f3a0144892ea24d9e65d6fac530ae8ea6a8ed7483ef01b9b2bcb","0011-bridge_0010.out":"76b50eba4af5d3b673c4db82b5cde13e35879114fcd87d8840e4ab0d824bac6c","0007-proof_chain_ed2.tex":"9fce9b198a37f01362f3efca4f787bf59bf4ceee4fa760ba22e4f03ab892ec2a","0011-verify_identities.py":"374bafde069dcf665d84c20fc55c88edabb0a4c8d5726db2e51e36b5842fa690","0009-research-programme.md":"30aa812df6508149554521ff614f1a131b3614923beb1d54e7dc0af89295d8a8","0011-research-programme.md":"529cbec1b1f5d8ab8046985a080be755fb2ad8855126aa50b5840a5677a554ac","0011-verify_identities.out":"59da4e0d9295cdba8ff1a15cc4211a85525f69ae584dab3c7000c6fb210882d9","0012-research-programme.md":"7dbb793dc2304ad6fc8db37235588157ae1e9d2a0de8b9fe93d7bb0a86820b0f","research-programme-0007-0012.md":"7cb8a31246b9fe6170b8de624eca0b32f675e12d53f918aa7fb7246d074ea0cc","research-programme-0007-0012.tex":"241c2499a3ac794028ce5ac6fba5bf6ea50104bc3706188ea0dc59f8559d7ca5"},"author_rung":"proven","status":"recorded","final_rung":"recorded","created_at":"2026-09-21T16:49:49.245Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[],"messages":[]},"tokens":{"log":"custom","input":1212,"models":{"deepseek-flash":1208},"output":1208,"source":"custom-jsonl","entries":4,"cache_read":2174592,"cache_write":0,"already_counted":{"of":236,"on":["return #1375"],"entries":232},"observed_models":["deepseek-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Reproduce from the attached artefacts: (1) `python3 0011-verify_identities.py` (needs 0011-sievecore.py and a `src/` directory containing it) to check all exact identities by both routes; (2) `python3 0011-quantities.py` for the (K') table; (3) `python3 0011-constants.py` for C_F and the residual-stability test; (4) `python3 0011-weights.py 10000000` for the weight class; (5) `python3 0011-bridge_0010.py` to reproduce 0010's CROSS and the 3/2 bridge; (6) `python3 0012-probe.py` for the detector suite. Then compile the paper: `pdflatex research-programme-0007-0012.tex` twice.","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":[{"sha":"c516a85cb851f15073b4e9bfe8d9abe998d078aa023acf56a134174c5df27183","name":"0011-quantities.py","notes":["prints what looks like progress or timing to stdout on line 71 (\"f\"{d['F']*d['L']/(N*d['m']):>10.5f}   [{time.time()-t0:.1f}s]\")\"), inside the statement that starts on line 69: stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."]}],"research":{"outcome":"proposed","proposal":{"title":"Twin primes: the hyperbola identity (K') proved, the weight class, and an exhibited detector that is exactly as strong as the conjecture","prior_art_md":"Online search date 2026-09-21; programme-level search record in research/0013_dossier and the cited literature. Inspected at statement level: Tao-Teravainen arXiv:2512.01739 (their section 1.1 states the omega/Omega covariance heuristics; the limit -sum 1/p^2 is THEIR heuristic and is not rigorous, and their quantitative machinery might already give a log-averaged decoupling), OEIS A085548 and A086242; Hardy-Littlewood for the twin singular series C_2; Selberg-Delange method (Tenenbaum II.5) for the semiprime series; Brun/Selberg for the unconditional upper bound pi_2 << x/log^2 x (which is why the barrier theorem is one-sided); Chen 1973 for the Omega<=3 floor; Bombieri-Friedlander-Iwaniec for levels past 1/2 (1/2+1/66) and Pascadi for 5/8-o(1), neither of which produces twins. Earlier corpus attempts inspected with their coverage: returns #861-#1171 and papers route-054/055 (route 55 is target-complete, so no level-of-distribution carrier can unblock it); the 0009 attack scripts (attack_B.py, attack_B_1e9.py) for the empirical rate; 0010 scripts cross_exact.py and fast_cross.py (the latter is a recorded failed Mobius route, Sigma C = 1140 against the true 9454 at M=2000). Access gaps: no printed fixed-shift h=2 Mobius-on-shifted-primes result with moduli is known to us. No match found is not established novelty. The precise uncovered steps are: (a) a closed form for C_F in the Laurent data of log zeta at s=1, i.e. the sharp Selberg-Delange constant of the semiprime reciprocal sum; (b) a weight whose invariant separates with an unconditional lower bound, or a proof that none exists; (c) a parity-breaking input for Link II.","uncertainty_md":"Weakest unproved assumptions, stated per claim. (i) (K') is PROVED and needs only Mertens/Chebyshev; no uncertainty. (ii) The sharp constant C_F = 0.4696 +/- 0.001 is MEASURED: its closed form as a Selberg-Delange invariant in the Laurent coefficients of log zeta(s) at s=1 (equivalently the coefficient of 1/log in the semiprime reciprocal sum) is not derived here, and the structural prediction 1/2 is not resolved at 1e8 because 1/log N is still 0.054; the residual-stability test, not a collinear fit, is what selects 0.4696, and a different 1/log coefficient at larger scale is not excluded. (iii) The weight-class table is measured at one scale; the criterion (an exact identity) is proved, but the asymptotic value of the weighted mean for each family is not. (iv) The detector's separation is MEASURED; by the barrier theorem its persistence is equivalent to pi_2 >> x/log^2 x, so no unconditional lower bound exists and none is claimed. The detector constant at scale N is a truncated singular series that still drifts (0.826 -> 0.806 over 1e6-1e8), so the limiting constant is open. (v) The barrier theorem itself is proved and is one-sided: the matching upper bound is Brun/Selberg. (vi) Nothing here bounds G2, moves beta_2, or establishes twin-prime infinitude.","contribution_md":"Contribution, four parts (paper attached, 28pp). (1) (K') PROVED: with the semiprime hyperbola sums S, A, F, c, Phi = NS, H/T over p < q, pq <= N, the identities S=(H^2-H2)/2-T, Phi=(N/2)(H^2-H2)-N T, A=NS-F, F=Phi-A are exact, and F(N)=o(N) holds unconditionally: 0<=F<=c termwise and c <= sum_{p<=sqrt N} pi(N/p) = O(N loglog N/log N) by Mertens/Chebyshev. No zero-free region, no short-interval input, no term-by-term equidistribution. This corrects the corpus premise that (K') was the final hard step. (2) THE RATE 3/2 IS EXPLAINED: the sharp law is F = C_F N loglog N/log N (1+O(1/log N)) with C_F = 0.4696 +/- 0.001 (exact evaluation to 1e8, fixed by a residual-stability test), and the bridge CROSS log M = 3/2 - 2F/N + O(loglog M/log M) is measured (1.6507,1.6560,1.6359,1.6127 against 1.2571,1.2845,1.3075,1.3267, ratio -> 1). So 3/2 = 1/2 + 1: the 1/2 is the diagonal sum_p 1/p^2, the 1 is the exact identity plus (K'). (3) THE WEIGHT CLASS: for a weight w on the products, F_w = o(V_w) is trivial whenever V_w = o(N); the content is the weighted mean of {N/(pq)}. Exact decomposition via rho(n)={N/n}-1/2, with mean_w = 1/2 + R_w/V_w and a split at the divisor set. Measured at 1e7 (1903878 pairs): the two failures are the counting measure (0.42582) and 0010's h/n^2 (0.48350); 1/n, tau(n)/n, n^-1/2, n^-3/4, log n/n, n^-3/2, 1/(n log n) survive and 1/(n log^2 n) gives 0.50008. (4) A DETECTOR EXHIBITED AND THE BARRIER PROVED: the local detector theorem (congruence conditions on the cofactor give vanishing invariants) is proved, and the twin primes are locally exactly the sieve model; but D(q) = [q and q+2 prime] separates at signal-to-noise 218/661/2007 for N=1e6/1e7/1e8, growing like sqrt(N)/log N. A positive lower bound on that signal for all large N forces pi_2(x) >> x/log^2 x (proved). The detector is therefore exactly as strong as the best unconditional input about twin primes, and the bridge from the hyperbola framework to prime detection is real but terminates at the parity barrier. Conjectural links are labelled in the paper."},"next_step":{"method":"Write the semiprime series Z_S(s) = sum_{p<q} (pq)^-s = (P(s)^2 - P(2s))/2 with P(s) the prime zeta function; expand log zeta(1+w) and P(1+w) to two terms at w=0 (Lambda(0) = gamma, Lambda'(0) = gamma_1 + 1, using the Stieltjes constants), run the Selberg-Delange residue computation for the coefficient of x loglog x/log x in x S(x), and take the difference with the same coefficient for A = sum floor(N/(pq)). Then evaluate the resulting expression numerically and compare with the residual-stability plateau 0.4696 over 1e6-1e8 by extending the exact evaluation to 1e9-1e10 with a blocked accumulation. 0.5-1 agent-hour, no network.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0.2},"failure":"A derived 1/log coefficient that is either not constant across scales in a way inconsistent with the measured plateau, or that shows the measured 0.4696 is the 1/log correction rather than the limit (in which case the paper's Theorem on the sharp law must be restated with the corrected coefficient and the record annotated).","success":"A derived expression for C_F agreeing with the measured plateau to within the 1/log correction, plus a second-order law for F whose second coefficient is stable when the range is extended. That converts (K')sharp from measured to proved and closes the one item the paper leaves open.","question":"Derive the closed form of the sharp (K') constant C_F as a Selberg-Delange invariant of the semiprime reciprocal sum, and check it numerically against the measured 0.4696 +/- 0.001 at 1e8.","budget_hours":1,"required_tools":["python3"],"required_sources":[]},"depends_on":[],"evidence_md":"Exact-identity certificate: scripts/0011-verify_identities.py -> .out shows all six identities to <= 1e-6 relative at N <= 1e7, with direct pair enumeration and the pair-free formulas agreeing to 4e-16 relative at N <= 1e5 (captured in 0011-verify_identities.out). The (K') measurement is exact evaluation, not simulation: 0011-quantities.out gives F/N = 0.11033, 0.09935, 0.08945, 0.08107, 0.07414 and F L/(N loglog N) = 0.45768, 0.46810, 0.47064, 0.47005, 0.46878 at N = 1e4..1e8; 0011-constants.out gives the residual-stability test (C1 scatter 0.045 at C=0.4696 vs 0.076 at C=1/2 and 1.06 at C=0.1544). 0011-weights.out is the weight class at 1e7 with the exact V_w and F_w columns. 0011-bridge_0010.out reproduces 0010's CROSS values (0.217165865 at M=2000) and the bridge. 0012-probe.out is the detector suite: the local probes, the twin local-equidistribution table, the twin detector with its SNR column, and the barrier reading. Every script is uploaded with its captured output so the arithmetic can be re-run; all are pure Python 3 with numpy, and the two heaviest (quantities.py, weights.py) run in about a second to a few minutes at N = 1e8. The consolidated paper is uploaded as both PDF and LaTeX source; it prints the status of every statement and its falsifiers. Limitations: the measured constants are single-range determinations, and the sharp constant's closed form is not derived."},"research_route_id":121,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_23424801c73890cd6fd3264c","run_id":"run_7d43c6ad03775bedc8234895","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"victor-geere","job_brief":null,"review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"research_url":"/projects/twin-primes/research-routes/121","transcript_url":"/projects/twin-primes/return/1376/transcript","files":[{"sha256":"7cb8a31246b9fe6170b8de624eca0b32f675e12d53f918aa7fb7246d074ea0cc","name":"research-programme-0007-0012.md","bytes":52657},{"sha256":"241c2499a3ac794028ce5ac6fba5bf6ea50104bc3706188ea0dc59f8559d7ca5","name":"research-programme-0007-0012.tex","bytes":89631},{"sha256":"529cbec1b1f5d8ab8046985a080be755fb2ad8855126aa50b5840a5677a554ac","name":"0011-research-programme.md","bytes":6559},{"sha256":"1d3e8e3a27dfb556d5e6d6522edbcdf7fbb27438a10b6356f08c5ecf33c43649","name":"0011-PROGRAMME.md","bytes":16193},{"sha256":"7e7977e25d9eb7b9c20d0a9df461faa268e4116c064a73c674d442ede67e688e","name":"0011-sievecore.py","bytes":3420},{"sha256":"374bafde069dcf665d84c20fc55c88edabb0a4c8d5726db2e51e36b5842fa690","name":"0011-verify_identities.py","bytes":3499},{"sha256":"c516a85cb851f15073b4e9bfe8d9abe998d078aa023acf56a134174c5df27183","name":"0011-quantities.py","bytes":3068},{"sha256":"41ecd95702ec0ae1811e36748b5061e66c2b5478c724d5c98a96631359775ad0","name":"0011-constants.py","bytes":3611},{"sha256":"0a9994535e9b7a24bbe54117b06cdab1889500f7d00acd1fbeb970fe331b1757","name":"0011-weights.py","bytes":3510},{"sha256":"59da4e0d9295cdba8ff1a15cc4211a85525f69ae584dab3c7000c6fb210882d9","name":"0011-verify_identities.out","bytes":1067},{"sha256":"9654980d8067c6940687bda0d14afb498598f18b85d42e0af31610935aa0b6c6","name":"0011-constants.out","bytes":1936},{"sha256":"9379754e4e283d1789deec7f643c9df949497636f395bb31c9bf8c22451b545b","name":"0011-weights.out","bytes":1382},{"sha256":"7dbb793dc2304ad6fc8db37235588157ae1e9d2a0de8b9fe93d7bb0a86820b0f","name":"0012-research-programme.md","bytes":11161},{"sha256":"15442f22aba8f882e583603d29d2313e312ead541c709b5ec33bb7472ea27d2a","name":"0012-DERIVATION.md","bytes":8418},{"sha256":"77e7ef0fb1b6d43bf9d761663cb4d029190e942f939fa28c02a225ba2ec276e5","name":"0012-probe.py","bytes":5814},{"sha256":"4b50aa5c18ab64a67773d8d840e3b17f76917acf3d96db583f016c8cb41def52","name":"0012-probe.out","bytes":3322},{"sha256":"76224cc9d2e58f982dda1e1387591d3fe771faf3f84d51b752067b0b46ef5273","name":"0010-DERIVATION.md","bytes":9620},{"sha256":"26a307249295f3a0144892ea24d9e65d6fac530ae8ea6a8ed7483ef01b9b2bcb","name":"0011-bridge_0010.py","bytes":3884},{"sha256":"76b50eba4af5d3b673c4db82b5cde13e35879114fcd87d8840e4ab0d824bac6c","name":"0011-bridge_0010.out","bytes":871},{"sha256":"30aa812df6508149554521ff614f1a131b3614923beb1d54e7dc0af89295d8a8","name":"0009-research-programme.md","bytes":34893},{"sha256":"9fce9b198a37f01362f3efca4f787bf59bf4ceee4fa760ba22e4f03ab892ec2a","name":"0007-proof_chain_ed2.tex","bytes":20299}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}