{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4NIVCFAMOVPOCZJTKIVZUHISSG","short_pith_number":"pith:4NIVCFAM","canonical_record":{"source":{"id":"1611.09815","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-11-29T20:06:41Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"7d21ca344371370d87bba2e06a52b27229071828e619d3c2e33a776009bf627e","abstract_canon_sha256":"b3a866773315b44fbd6831c12b76a13ea4cbede7708215d9af2d18554f6b88d5"},"schema_version":"1.0"},"canonical_sha256":"e35151140c755ee16533522b9a1d129187942ee5cee0c237ea417b9999bdc70d","source":{"kind":"arxiv","id":"1611.09815","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.09815","created_at":"2026-05-18T00:56:12Z"},{"alias_kind":"arxiv_version","alias_value":"1611.09815v1","created_at":"2026-05-18T00:56:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.09815","created_at":"2026-05-18T00:56:12Z"},{"alias_kind":"pith_short_12","alias_value":"4NIVCFAMOVPO","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4NIVCFAMOVPOCZJT","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4NIVCFAM","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4NIVCFAMOVPOCZJTKIVZUHISSG","target":"record","payload":{"canonical_record":{"source":{"id":"1611.09815","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-11-29T20:06:41Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"7d21ca344371370d87bba2e06a52b27229071828e619d3c2e33a776009bf627e","abstract_canon_sha256":"b3a866773315b44fbd6831c12b76a13ea4cbede7708215d9af2d18554f6b88d5"},"schema_version":"1.0"},"canonical_sha256":"e35151140c755ee16533522b9a1d129187942ee5cee0c237ea417b9999bdc70d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:12.918774Z","signature_b64":"vgc4FqVkZghdzqKNTSil+S9IaRFT84L1tLQRpo4JlpK2Gn7Stn86jdhbNZkcptP+UdX+i3ToWqV+6HQD3jKvBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e35151140c755ee16533522b9a1d129187942ee5cee0c237ea417b9999bdc70d","last_reissued_at":"2026-05-18T00:56:12.918110Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:12.918110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.09815","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:56:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/xhBWkr3nuZ9R/RN9Fy7kCuPawepJDDudo/92hOqPVoJuNpzgfEePBtT5cxMvIvyULVy3U7Anbm/nf5mhWh2Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:21:44.374880Z"},"content_sha256":"954a35fa15ceb29a6d5ed9de9de7a9364d0cab17076da5b62e97d1034b96700d","schema_version":"1.0","event_id":"sha256:954a35fa15ceb29a6d5ed9de9de7a9364d0cab17076da5b62e97d1034b96700d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4NIVCFAMOVPOCZJTKIVZUHISSG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The term a_4 in the heat kernel expansion of noncommutative tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"math.QA","authors_text":"Alain Connes, Farzad Fathizadeh","submitted_at":"2016-11-29T20:06:41Z","abstract_excerpt":"We consider the Laplacian associated with a general metric in the canonical conformal structure of the noncommutative two torus, and calculate a local expression for the term a_4 that appears in its corresponding small-time heat kernel expansion. The final formula involves one variable functions and lengthy two, three and four variable functions of the modular automorphism of the state that encodes the conformal perturbation of the flat metric. We confirm the validity of the calculated expressions by showing that they satisfy a family of conceptually predicted functional relations. By studying"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09815","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:56:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"biYGX9KSgIWTGg3c9WGhyXzv6MqMaok1JotMGT4ofglwzitJgD42gDpYmQI1l/fNObmIaKq8tQ9oM0I54lCgBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:21:44.375507Z"},"content_sha256":"42d77e0f64b8a7ea0fbfbf70cf613d80870da87eb8c90bf4f8265a1853f7b3f2","schema_version":"1.0","event_id":"sha256:42d77e0f64b8a7ea0fbfbf70cf613d80870da87eb8c90bf4f8265a1853f7b3f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4NIVCFAMOVPOCZJTKIVZUHISSG/bundle.json","state_url":"https://pith.science/pith/4NIVCFAMOVPOCZJTKIVZUHISSG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4NIVCFAMOVPOCZJTKIVZUHISSG/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":"2026-05-28T05:21:44Z","links":{"resolver":"https://pith.science/pith/4NIVCFAMOVPOCZJTKIVZUHISSG","bundle":"https://pith.science/pith/4NIVCFAMOVPOCZJTKIVZUHISSG/bundle.json","state":"https://pith.science/pith/4NIVCFAMOVPOCZJTKIVZUHISSG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4NIVCFAMOVPOCZJTKIVZUHISSG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4NIVCFAMOVPOCZJTKIVZUHISSG","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":"b3a866773315b44fbd6831c12b76a13ea4cbede7708215d9af2d18554f6b88d5","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-11-29T20:06:41Z","title_canon_sha256":"7d21ca344371370d87bba2e06a52b27229071828e619d3c2e33a776009bf627e"},"schema_version":"1.0","source":{"id":"1611.09815","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.09815","created_at":"2026-05-18T00:56:12Z"},{"alias_kind":"arxiv_version","alias_value":"1611.09815v1","created_at":"2026-05-18T00:56:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.09815","created_at":"2026-05-18T00:56:12Z"},{"alias_kind":"pith_short_12","alias_value":"4NIVCFAMOVPO","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4NIVCFAMOVPOCZJT","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4NIVCFAM","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:42d77e0f64b8a7ea0fbfbf70cf613d80870da87eb8c90bf4f8265a1853f7b3f2","target":"graph","created_at":"2026-05-18T00:56:12Z","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"},"paper":{"abstract_excerpt":"We consider the Laplacian associated with a general metric in the canonical conformal structure of the noncommutative two torus, and calculate a local expression for the term a_4 that appears in its corresponding small-time heat kernel expansion. The final formula involves one variable functions and lengthy two, three and four variable functions of the modular automorphism of the state that encodes the conformal perturbation of the flat metric. We confirm the validity of the calculated expressions by showing that they satisfy a family of conceptually predicted functional relations. By studying","authors_text":"Alain Connes, Farzad Fathizadeh","cross_cats":["math-ph","math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-11-29T20:06:41Z","title":"The term a_4 in the heat kernel expansion of noncommutative tori"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09815","kind":"arxiv","version":1},"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":"sha256:954a35fa15ceb29a6d5ed9de9de7a9364d0cab17076da5b62e97d1034b96700d","target":"record","created_at":"2026-05-18T00:56:12Z","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":"b3a866773315b44fbd6831c12b76a13ea4cbede7708215d9af2d18554f6b88d5","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-11-29T20:06:41Z","title_canon_sha256":"7d21ca344371370d87bba2e06a52b27229071828e619d3c2e33a776009bf627e"},"schema_version":"1.0","source":{"id":"1611.09815","kind":"arxiv","version":1}},"canonical_sha256":"e35151140c755ee16533522b9a1d129187942ee5cee0c237ea417b9999bdc70d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e35151140c755ee16533522b9a1d129187942ee5cee0c237ea417b9999bdc70d","first_computed_at":"2026-05-18T00:56:12.918110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:12.918110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vgc4FqVkZghdzqKNTSil+S9IaRFT84L1tLQRpo4JlpK2Gn7Stn86jdhbNZkcptP+UdX+i3ToWqV+6HQD3jKvBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:12.918774Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.09815","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:954a35fa15ceb29a6d5ed9de9de7a9364d0cab17076da5b62e97d1034b96700d","sha256:42d77e0f64b8a7ea0fbfbf70cf613d80870da87eb8c90bf4f8265a1853f7b3f2"],"state_sha256":"f675527c6f645e2f93cb57a8dcb121059064a3d21dce34808b0b26cd5abba32b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"29sLcirTamFCj2pe5tmW4djmBfjl0AM0Ol+5bwMpXAEY63fQpbtCtixsLNuKPGi0UkIUCCSLvVeZlC9F3jrCDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T05:21:44.378428Z","bundle_sha256":"16cd4e0334773a5477319d47bb1b817096401dc098d0c1a6d54ecbf203911de5"}}