TFPT scientific source excerpt Original repository path: experiments/theory-contracts/native-octic-seam-origin-20261025/DOCUMENTATION-COVERAGE.txt Original file SHA-256: 0a05d552ac64a5e9d36ec17d192689839286687064a543ed8373b7f59498c194 Inclusive original lines: 1-138 Line numbers below refer to the original source. This bounded excerpt is source evidence; it is not a new proof/checker run. Conversation metadata and personal execution details are omitted where indicated. 000001 | DOCUMENTATION COVERAGE OF THE ORIGINAL OCTIC SOURCE RESULTS 000002 | ========================================================== 000003 | 000004 | 25 October 2026. This index documents the exact scope of the current 000005 | results. It adds no physical promotion and is not another proof source. 000006 | The proofs, executable and original input records listed below remain 000007 | authoritative. The complete source contract retains verdict PARTIAL. 000008 | 000009 | 1. Original shifted-source response 000010 | ------------------------------------ 000011 | Claim: MATH.NATIVE.FOLDED-OCTIC-WARD.01 000012 | Atlas: finding:actual-quarter-fold-stress-has-nonzero-octic-eighth-jet 000013 | 000014 | The fixed original M/O/U+ maps give nonzero F8hat(b) in both actual 000015 | quarter sectors. The exact matrix element is 000016 | 000017 | =8! conjugate(F8hat(b)). 000018 | 000019 | The old null theorem remains valid for the different UNSHIFTED pair 000020 | Omega,L_n. It is not extended to Omega_d,L_n^d. This correction preserves 000021 | the old theorem and removes the overbroad origin exclusion. 000022 | 000023 | Proof: NATIVE-FOLDED-OCTIC-ORIGIN.txt, sections1-3. 000024 | Executable: native_folded_octic_origin.py, original_transport and main. 000025 | Results: native_folded_octic_origin_results.json, both quarter cases. 000026 | 000027 | 2. Complete words, unitary orbit and genuine local profiles 000028 | ----------------------------------------------------------- 000029 | Same claim and Atlas finding as item1. 000030 | 000031 | All22 oscillator partitions at level8 are retained. The derivation 000032 | recursion and complete Bell partition formula independently give the 000033 | full descendant norm8!(85/128)_8. The unshifted zero-shift control passes. 000034 | The Mobius orbit includes every higher level and is normalized. 000035 | 000036 | For smooth real local stress A_d(g), all response jets k<8 vanish, while 000037 | the eighth is8!conjugate(F8hat(b))c_-1^8. If c_-1 is nonzero, the exact 000038 | unitary amplitude starts at order t^8; its probability starts at t^16. 000039 | Real smooth local bumps with this property exist in any proper fold 000040 | interval. Their infinite Fourier tails are retained. The proof uses 000041 | finite-order differentiability, not an assumed entire analytic vector. 000042 | 000043 | Proof: LOCAL-STRESS-HISTORY.txt, sections2-3. 000044 | Executable: full_translation_descendants in the same checker. 000045 | 000046 | 3. Direct original even CAR realization 000047 | ---------------------------------------- 000048 | Claim: MATH.NATIVE.OCTIC-CAR-COMPOSITE.01 000049 | Atlas: finding:native-octic-is-an-original-even-car-current-composite 000050 | 000051 | A=U+^T O^T M obeys AA*=I4 and AA^T=0. The literal field is 000052 | 000053 | :I8(A(j_sea(z)+delta/z))/(96 sqrt140):. 000054 | 000055 | It is an original neutral even CAR current composite. The same source 000056 | covariance, point splitting, finite derivative counterterms and adjoints 000057 | are used. A full E8 root/spinor charge extension is NOT required for this 000058 | mechanism. The colon is current normal order, not a naive fermionically 000059 | normal-ordered degree16 monomial. The fold excitation energy8 corresponds 000060 | to original source excitation energy64; this is not a unit in seconds. 000061 | 000062 | Proof: CAR-OCTIC-DICTIONARY.txt. 000063 | Original prescription: joint-native-algebra-selection-20261016/ 000064 | ORIGINAL-ORDERED-CURRENT-KERNEL-AND-SEAM-GRADING.txt:108-160. 000065 | Executable/results: direct_original_car_current_dictionary. 000066 | 000067 | 4. Geometric jet and the positive source properties 000068 | --------------------------------------------------- 000069 | Claim: MATH.NATIVE.GEOMETRIC-SOURCE-JET.01 000070 | Atlas: finding:original-geometric-source-jet-and-partial-p1-seed-closure 000071 | 000072 | The actual half-density pullback derives the one-particle source jet. 000073 | Twisted and periodic charts are gauge transported together; the periodic 000074 | jet includes -alpha v'. The fold profile lifts to eight original arcs. 000075 | The original positive CAR Hamiltonian supplies the bounded even OS 000076 | history form and Euclidean imaginary-time clustering. The original seam 000077 | has winding and spectral flow+1. No real-time decay is inferred. 000078 | 000079 | Proofs: GEOMETRIC-SOURCE-JET.txt and P1-SOURCE-EMBEDDING-AUDIT.txt. 000080 | The elementary matrix, derivative and source checks are recorded in 000081 | those proofs; the checker tests the original M/O/current identities. 000082 | 000083 | 5. Bounded full-root OPE component in the optional larger algebra 000084 | ---------------------------------------------------------------- 000085 | Claim: MATH.NATIVE.ROOT-OCTIC-COMPONENT.01 000086 | Atlas: finding:full-root-ope-has-normalized-native-octic-component 000087 | 000088 | This separate result assumes the supplied full E8 vertex algebra. Its 000089 | phase-correct dual-root product has a full weight8 coefficient S8, with 000090 | all22 oscillator partitions. The original positive polarization gives 000091 | zero root moments2,4,6 and moment8=(15/2)I8. Exactly, 000092 | 000093 | =sqrt140/56=sqrt35/28, 000094 | ||S8||^2=15600. 000095 | 000096 | This is a component statement; no exclusivity or physical projection is 000097 | proved. The classical octic/root invariant identity is not claimed as 000098 | new invariant theory. This larger algebra is not a premise of item3. 000099 | 000100 | Proof: NATIVE-FOLDED-OCTIC-ORIGIN.txt, section4. 000101 | Executable/results: root_ope_bounded_result in the same checker/output. 000102 | 000103 | 6. Precisely retained open boundary 000104 | ------------------------------------ 000105 | The same source-to-P1 map must intertwine the local net, positive-time 000106 | localization, state and seam, and simultaneously identify Theta, 000107 | D_coll and D_ref with the ORIGINAL P1 data, including domains and eta. 000108 | The available diagnostic angular zeta reference is explicitly not D_ref. 000109 | Choosing a new product collar or reference would not prove that identity. 000110 | 000111 | Experimental profiles and pulse strengths are intervention inputs, not 000112 | missing fundamental constants. A nonzero F8 component neither prepares 000113 | only F8 nor constructs a six-outcome measurement instrument. The local 000114 | P1 comparison does not by itself solve every full 3+1-dimensional field, 000115 | matter, gravity or initial-state obligation. 000116 | 000117 | Open task: task:derive-original-seam-selection-of-native-observable-process. 000118 | Full comparison proof: P1-SOURCE-EMBEDDING-AUDIT.txt, section7. 000119 | 000120 | 7. Reproduction and persistence 000121 | -------------------------------- 000122 | The preceding research turn executed normal and python -OO versions of 000123 | the exact checker. Their saved JSON outputs were byte identical. This 000124 | documentation task rechecks the retained output equality and every 000125 | current reviewed source SHA256/line range; it does not present that 000126 | persistence check as another independent mathematical experiment. 000127 | 000128 | Reproduce the exact computation from the repository root with 000129 | 000130 | python3 experiments/theory-contracts/native-octic-seam-origin-20261025/native_folded_octic_origin.py 000131 | python3 -OO experiments/theory-contracts/native-octic-seam-origin-20261025/native_folded_octic_origin.py 000132 | 000133 | The canonical reviewed Atlas problem is 000134 | problem:atlas-clock-defect-and-operational-reconstruction. 000135 | The contract_index.json registers all four claim IDs. Atlas records retain 000136 | premises, scoped negatives, proof references, SHA256 and line ranges. 000137 | The independent explanatory images are illustrations of this state, 000138 | never evidence or a percentage estimate of total physical completion.