{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:X6AEBDAWTPN73Z3M34J5UGH2HJ","short_pith_number":"pith:X6AEBDAW","canonical_record":{"source":{"id":"1611.01815","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-06T18:06:53Z","cross_cats_sorted":["math.AG","math.DG","math.MP"],"title_canon_sha256":"c66ca9106623d91b779c5de91606f33ef1fb124e4e4b6dd1085408a98a0c64f5","abstract_canon_sha256":"f51220774e8c9cc6378efdf6d9f2b2ac867143fed2b37b2ab3a5f9864cdacdb2"},"schema_version":"1.0"},"canonical_sha256":"bf80408c169bdbfde76cdf13da18fa3a413c3f18de9eb165ceb547392ba61e6c","source":{"kind":"arxiv","id":"1611.01815","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.01815","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"arxiv_version","alias_value":"1611.01815v1","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01815","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"pith_short_12","alias_value":"X6AEBDAWTPN7","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"X6AEBDAWTPN73Z3M","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"X6AEBDAW","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:X6AEBDAWTPN73Z3M34J5UGH2HJ","target":"record","payload":{"canonical_record":{"source":{"id":"1611.01815","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-06T18:06:53Z","cross_cats_sorted":["math.AG","math.DG","math.MP"],"title_canon_sha256":"c66ca9106623d91b779c5de91606f33ef1fb124e4e4b6dd1085408a98a0c64f5","abstract_canon_sha256":"f51220774e8c9cc6378efdf6d9f2b2ac867143fed2b37b2ab3a5f9864cdacdb2"},"schema_version":"1.0"},"canonical_sha256":"bf80408c169bdbfde76cdf13da18fa3a413c3f18de9eb165ceb547392ba61e6c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:14.445778Z","signature_b64":"IjfkJ+zZ7/Gvqj8Spcq8YPKCXPQ94BJ7QqCJ2VY736aU++QI/aH0CnRN3bYLAYvcJqp7JAlgxjGiTsCkVqtWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf80408c169bdbfde76cdf13da18fa3a413c3f18de9eb165ceb547392ba61e6c","last_reissued_at":"2026-05-18T00:32:14.445155Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:14.445155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.01815","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":"2026-05-18T00:32:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bqQ5LsH9bNTmA9begYrejqIjb+oQY23oCMIt70v0zCh2hPSTL61h7NEY67OJmQSaaShS7sXIL6xUCrNWuovBCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:44:41.738994Z"},"content_sha256":"c8f884882271e4c7f069f87a0c75db5fc7d534676f648132c00416b7d4cd911d","schema_version":"1.0","event_id":"sha256:c8f884882271e4c7f069f87a0c75db5fc7d534676f648132c00416b7d4cd911d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:X6AEBDAWTPN73Z3M34J5UGH2HJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Periods and motives in the spectral action of Robertson-Walker spacetimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"Farzad Fathizadeh, Matilde Marcolli","submitted_at":"2016-11-06T18:06:53Z","abstract_excerpt":"We show that, when considering the scaling factor as an affine variable, the coefficients of the asymptotic expansion of the spectral action on a (Euclidean) Robertson-Walker spacetime are periods of mixed Tate motives, involving relative motives of complements of unions of hyperplanes and quadric hypersurfaces and divisors given by unions of coordinate hyperplanes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01815","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":"2026-05-18T00:32:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qqtp+spxiMFiGNZupjwM5kpKMZj1vNr5PQ6dtep1IU23OstofdHLuvqQaEaRQ6cjv5vTilvR+bwk7L1TRR/kDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:44:41.739633Z"},"content_sha256":"7ade341822b541357fe353c32aa8f612032cdf937439b2db6a063d3eac4953c2","schema_version":"1.0","event_id":"sha256:7ade341822b541357fe353c32aa8f612032cdf937439b2db6a063d3eac4953c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X6AEBDAWTPN73Z3M34J5UGH2HJ/bundle.json","state_url":"https://pith.science/pith/X6AEBDAWTPN73Z3M34J5UGH2HJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X6AEBDAWTPN73Z3M34J5UGH2HJ/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":"2026-05-28T06:44:41Z","links":{"resolver":"https://pith.science/pith/X6AEBDAWTPN73Z3M34J5UGH2HJ","bundle":"https://pith.science/pith/X6AEBDAWTPN73Z3M34J5UGH2HJ/bundle.json","state":"https://pith.science/pith/X6AEBDAWTPN73Z3M34J5UGH2HJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X6AEBDAWTPN73Z3M34J5UGH2HJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:X6AEBDAWTPN73Z3M34J5UGH2HJ","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":"f51220774e8c9cc6378efdf6d9f2b2ac867143fed2b37b2ab3a5f9864cdacdb2","cross_cats_sorted":["math.AG","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-06T18:06:53Z","title_canon_sha256":"c66ca9106623d91b779c5de91606f33ef1fb124e4e4b6dd1085408a98a0c64f5"},"schema_version":"1.0","source":{"id":"1611.01815","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.01815","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"arxiv_version","alias_value":"1611.01815v1","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01815","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"pith_short_12","alias_value":"X6AEBDAWTPN7","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"X6AEBDAWTPN73Z3M","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"X6AEBDAW","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:7ade341822b541357fe353c32aa8f612032cdf937439b2db6a063d3eac4953c2","target":"graph","created_at":"2026-05-18T00:32:14Z","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 show that, when considering the scaling factor as an affine variable, the coefficients of the asymptotic expansion of the spectral action on a (Euclidean) Robertson-Walker spacetime are periods of mixed Tate motives, involving relative motives of complements of unions of hyperplanes and quadric hypersurfaces and divisors given by unions of coordinate hyperplanes.","authors_text":"Farzad Fathizadeh, Matilde Marcolli","cross_cats":["math.AG","math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-06T18:06:53Z","title":"Periods and motives in the spectral action of Robertson-Walker spacetimes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01815","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:c8f884882271e4c7f069f87a0c75db5fc7d534676f648132c00416b7d4cd911d","target":"record","created_at":"2026-05-18T00:32:14Z","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":"f51220774e8c9cc6378efdf6d9f2b2ac867143fed2b37b2ab3a5f9864cdacdb2","cross_cats_sorted":["math.AG","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-06T18:06:53Z","title_canon_sha256":"c66ca9106623d91b779c5de91606f33ef1fb124e4e4b6dd1085408a98a0c64f5"},"schema_version":"1.0","source":{"id":"1611.01815","kind":"arxiv","version":1}},"canonical_sha256":"bf80408c169bdbfde76cdf13da18fa3a413c3f18de9eb165ceb547392ba61e6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf80408c169bdbfde76cdf13da18fa3a413c3f18de9eb165ceb547392ba61e6c","first_computed_at":"2026-05-18T00:32:14.445155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:14.445155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IjfkJ+zZ7/Gvqj8Spcq8YPKCXPQ94BJ7QqCJ2VY736aU++QI/aH0CnRN3bYLAYvcJqp7JAlgxjGiTsCkVqtWBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:14.445778Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.01815","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8f884882271e4c7f069f87a0c75db5fc7d534676f648132c00416b7d4cd911d","sha256:7ade341822b541357fe353c32aa8f612032cdf937439b2db6a063d3eac4953c2"],"state_sha256":"6311a57a0cf7c4b5801b6c28369b56538779afb957165544ba3d4edcb3b7feb2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4LpoGWOIQprPjwNT6uo7BXWYDwrI57AAtKTZUDfXf+ge/p5PExytNmi8lsGCZBubaCEDdZ2EaXVMIM3Uex+tAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T06:44:41.742629Z","bundle_sha256":"3e8d2121665b47bc5595d57b5367de8301394129365e910feb72ea3b5588ae21"}}