{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:5KFNHZDVJZQQUOH2QU24N3QP2C","short_pith_number":"pith:5KFNHZDV","canonical_record":{"source":{"id":"2512.13329","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-12-15T13:41:24Z","cross_cats_sorted":[],"title_canon_sha256":"3f375ec92ba7eb37d6c085e8e0c2d03708d08715982013450103646d8e8c82a6","abstract_canon_sha256":"d27684177210576bcf2e46a0442d8dc299fe6a35bf72184e58ff2c0b65f74afa"},"schema_version":"1.0"},"canonical_sha256":"ea8ad3e4754e610a38fa8535c6ee0fd0bfa372f7990b9429b1e23aa38e0a2fae","source":{"kind":"arxiv","id":"2512.13329","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.13329","created_at":"2026-05-21T01:04:19Z"},{"alias_kind":"arxiv_version","alias_value":"2512.13329v3","created_at":"2026-05-21T01:04:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.13329","created_at":"2026-05-21T01:04:19Z"},{"alias_kind":"pith_short_12","alias_value":"5KFNHZDVJZQQ","created_at":"2026-05-21T01:04:19Z"},{"alias_kind":"pith_short_16","alias_value":"5KFNHZDVJZQQUOH2","created_at":"2026-05-21T01:04:19Z"},{"alias_kind":"pith_short_8","alias_value":"5KFNHZDV","created_at":"2026-05-21T01:04:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:5KFNHZDVJZQQUOH2QU24N3QP2C","target":"record","payload":{"canonical_record":{"source":{"id":"2512.13329","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-12-15T13:41:24Z","cross_cats_sorted":[],"title_canon_sha256":"3f375ec92ba7eb37d6c085e8e0c2d03708d08715982013450103646d8e8c82a6","abstract_canon_sha256":"d27684177210576bcf2e46a0442d8dc299fe6a35bf72184e58ff2c0b65f74afa"},"schema_version":"1.0"},"canonical_sha256":"ea8ad3e4754e610a38fa8535c6ee0fd0bfa372f7990b9429b1e23aa38e0a2fae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:04:19.910884Z","signature_b64":"vEvQQjTPYf/N7+i0gG+PKAVOwHArwHggBJHsjQGiagPjZwKHJBJQyWFCM8lN7TwWVgncsmAOEtHzKfCC4/DqCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea8ad3e4754e610a38fa8535c6ee0fd0bfa372f7990b9429b1e23aa38e0a2fae","last_reissued_at":"2026-05-21T01:04:19.910003Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:04:19.910003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2512.13329","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-21T01:04:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TsNgT/VWt0OdwJNOyIDv3yyBH1Dw4vr7GQ2DsnFHSjM9NiF9E7ail11yyENr6WE+ONEhgPsAwAM8gmfIUsTIBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:07:20.404952Z"},"content_sha256":"d1feb051bf5f5a43d9683f23acf9185594de77b5b521aada13c0562adb9275cb","schema_version":"1.0","event_id":"sha256:d1feb051bf5f5a43d9683f23acf9185594de77b5b521aada13c0562adb9275cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:5KFNHZDVJZQQUOH2QU24N3QP2C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tensors, Gaussians and the Alexander Polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Boudewijn Bosch","submitted_at":"2025-12-15T13:41:24Z","abstract_excerpt":"Building on the approach of Bar-Natan and Van der Veen to universal knot invariants using (perturbed) Gaussian functions, we develop a Gaussian model to compute the Alexander polynomial $\\Delta_{\\mathcal{K}}(T)$ of an oriented knot $\\mathcal{K}$ in $S^3$. Using the Heisenberg algebra and a tensor-contraction formalism, we associate to a knot a Gaussian function whose partition function recovers $\\Delta_{\\mathcal K}(T)$. Here, a presentation matrix of the Alexander module plays the role of a precision matrix of the Gaussian function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.13329","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.13329/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-21T01:04:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hl1J+QfLUfZuqggJqCcA9PPEERktvGGZJFeTr2RsGt2LhpdoJJI5TtjqKtdGo1O8CrQnIQ4rhT2STM3ftAItAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:07:20.405716Z"},"content_sha256":"f5990268a3f9aa259d46575c72a50b681ec0843a2a3cc6c4f458953adea51408","schema_version":"1.0","event_id":"sha256:f5990268a3f9aa259d46575c72a50b681ec0843a2a3cc6c4f458953adea51408"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5KFNHZDVJZQQUOH2QU24N3QP2C/bundle.json","state_url":"https://pith.science/pith/5KFNHZDVJZQQUOH2QU24N3QP2C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5KFNHZDVJZQQUOH2QU24N3QP2C/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T18:07:20Z","links":{"resolver":"https://pith.science/pith/5KFNHZDVJZQQUOH2QU24N3QP2C","bundle":"https://pith.science/pith/5KFNHZDVJZQQUOH2QU24N3QP2C/bundle.json","state":"https://pith.science/pith/5KFNHZDVJZQQUOH2QU24N3QP2C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5KFNHZDVJZQQUOH2QU24N3QP2C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:5KFNHZDVJZQQUOH2QU24N3QP2C","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d27684177210576bcf2e46a0442d8dc299fe6a35bf72184e58ff2c0b65f74afa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-12-15T13:41:24Z","title_canon_sha256":"3f375ec92ba7eb37d6c085e8e0c2d03708d08715982013450103646d8e8c82a6"},"schema_version":"1.0","source":{"id":"2512.13329","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.13329","created_at":"2026-05-21T01:04:19Z"},{"alias_kind":"arxiv_version","alias_value":"2512.13329v3","created_at":"2026-05-21T01:04:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.13329","created_at":"2026-05-21T01:04:19Z"},{"alias_kind":"pith_short_12","alias_value":"5KFNHZDVJZQQ","created_at":"2026-05-21T01:04:19Z"},{"alias_kind":"pith_short_16","alias_value":"5KFNHZDVJZQQUOH2","created_at":"2026-05-21T01:04:19Z"},{"alias_kind":"pith_short_8","alias_value":"5KFNHZDV","created_at":"2026-05-21T01:04:19Z"}],"graph_snapshots":[{"event_id":"sha256:f5990268a3f9aa259d46575c72a50b681ec0843a2a3cc6c4f458953adea51408","target":"graph","created_at":"2026-05-21T01:04:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2512.13329/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Building on the approach of Bar-Natan and Van der Veen to universal knot invariants using (perturbed) Gaussian functions, we develop a Gaussian model to compute the Alexander polynomial $\\Delta_{\\mathcal{K}}(T)$ of an oriented knot $\\mathcal{K}$ in $S^3$. Using the Heisenberg algebra and a tensor-contraction formalism, we associate to a knot a Gaussian function whose partition function recovers $\\Delta_{\\mathcal K}(T)$. Here, a presentation matrix of the Alexander module plays the role of a precision matrix of the Gaussian function.","authors_text":"Boudewijn Bosch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-12-15T13:41:24Z","title":"Tensors, Gaussians and the Alexander Polynomial"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.13329","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d1feb051bf5f5a43d9683f23acf9185594de77b5b521aada13c0562adb9275cb","target":"record","created_at":"2026-05-21T01:04:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d27684177210576bcf2e46a0442d8dc299fe6a35bf72184e58ff2c0b65f74afa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-12-15T13:41:24Z","title_canon_sha256":"3f375ec92ba7eb37d6c085e8e0c2d03708d08715982013450103646d8e8c82a6"},"schema_version":"1.0","source":{"id":"2512.13329","kind":"arxiv","version":3}},"canonical_sha256":"ea8ad3e4754e610a38fa8535c6ee0fd0bfa372f7990b9429b1e23aa38e0a2fae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea8ad3e4754e610a38fa8535c6ee0fd0bfa372f7990b9429b1e23aa38e0a2fae","first_computed_at":"2026-05-21T01:04:19.910003Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:04:19.910003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vEvQQjTPYf/N7+i0gG+PKAVOwHArwHggBJHsjQGiagPjZwKHJBJQyWFCM8lN7TwWVgncsmAOEtHzKfCC4/DqCA==","signature_status":"signed_v1","signed_at":"2026-05-21T01:04:19.910884Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.13329","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1feb051bf5f5a43d9683f23acf9185594de77b5b521aada13c0562adb9275cb","sha256:f5990268a3f9aa259d46575c72a50b681ec0843a2a3cc6c4f458953adea51408"],"state_sha256":"3499bc2938502c4788e11f1ce3a0909ad6c955c0ff63f2523abe2a1dfe135978"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6lJb7yBtgC8mivfkbC8BtqZw4tHifxx7a9m96JwLCvANsv4zOPSTFVlNmtgisjJM5cLXiCUGtEW9WRP0tiFYBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T18:07:20.409928Z","bundle_sha256":"6b505c6b10eae82096142c6d95957773440ef9c57fadbb0428515f9bd05dbc7e"}}