{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3LZN2QRDO4MXBQU76CLN7KWT6F","short_pith_number":"pith:3LZN2QRD","canonical_record":{"source":{"id":"1407.5972","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-07-22T18:56:18Z","cross_cats_sorted":["gr-qc","hep-th","math.MP","math.QA"],"title_canon_sha256":"934362b4a5a05c54122a3b2066a5bd7d883cd3c5b7337ec6d02ed9fdae32e561","abstract_canon_sha256":"a2ae8e4b555bd7e9c5360db70d20d8d111bec39c75dc4c32c624f67dca4a7275"},"schema_version":"1.0"},"canonical_sha256":"daf2dd4223771970c29ff096dfaad3f16d7f6b8c606f504176ecb5c98134c14c","source":{"kind":"arxiv","id":"1407.5972","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.5972","created_at":"2026-05-18T01:42:33Z"},{"alias_kind":"arxiv_version","alias_value":"1407.5972v2","created_at":"2026-05-18T01:42:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5972","created_at":"2026-05-18T01:42:33Z"},{"alias_kind":"pith_short_12","alias_value":"3LZN2QRDO4MX","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3LZN2QRDO4MXBQU7","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3LZN2QRD","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3LZN2QRDO4MXBQU76CLN7KWT6F","target":"record","payload":{"canonical_record":{"source":{"id":"1407.5972","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-07-22T18:56:18Z","cross_cats_sorted":["gr-qc","hep-th","math.MP","math.QA"],"title_canon_sha256":"934362b4a5a05c54122a3b2066a5bd7d883cd3c5b7337ec6d02ed9fdae32e561","abstract_canon_sha256":"a2ae8e4b555bd7e9c5360db70d20d8d111bec39c75dc4c32c624f67dca4a7275"},"schema_version":"1.0"},"canonical_sha256":"daf2dd4223771970c29ff096dfaad3f16d7f6b8c606f504176ecb5c98134c14c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:42:33.004756Z","signature_b64":"zkCo6AzlrI2uq4t0rTGqYhF57rjtrYfgYSI25IeU7G8u48x/NB7VZbBrK7cypnhGARnyhDU4WIhEcJY2gefiCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"daf2dd4223771970c29ff096dfaad3f16d7f6b8c606f504176ecb5c98134c14c","last_reissued_at":"2026-05-18T01:42:33.004285Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:42:33.004285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.5972","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:42:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YUTiZxJL188aQ9/0teAF6Bfvzt/Zvq/twFWe4z5JyWF4viZRN2HhMTfbaf1ymAP3jGuBNX1F8zoLa6sjMSPnAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:30:28.241237Z"},"content_sha256":"3728d2e39e09a79eea9be581aa356ff3b4f7be09316dc5e353b12bb61a4349aa","schema_version":"1.0","event_id":"sha256:3728d2e39e09a79eea9be581aa356ff3b4f7be09316dc5e353b12bb61a4349aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3LZN2QRDO4MXBQU76CLN7KWT6F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rationality of Spectral Action for Robertson-Walker Metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-th","math.MP","math.QA"],"primary_cat":"math-ph","authors_text":"Asghar Ghorbanpour, Farzad Fathizadeh, Masoud Khalkhali","submitted_at":"2014-07-22T18:56:18Z","abstract_excerpt":"We use pseudodifferential calculus and heat kernel techniques to prove a conjecture by Chamseddine and Connes on rationality of the coefficients of the polynomials in the cosmic scale factor $a(t)$ and its higher derivatives, which describe the general terms $a_{2n}$ in the expansion of the spectral action for general Robertson-Walker metrics. We also compute the terms up to $a_{12}$ in the expansion of the spectral action by our method. As a byproduct, we verify that our computations agree with the terms up to $a_{10}$ that were previously computed by Chamseddine and Connes by a different met"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5972","kind":"arxiv","version":2},"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":"2026-05-18T01:42:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3BXlbwWbPOfwx8w02MVwcdYREDOp5g3sb1pBpHfOrexVCIpXk+0hSV73uG373/yrbxvpuGqf6hrSVG4qJeriCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:30:28.241601Z"},"content_sha256":"f93e99d3946e70cfb19e2e698591abbb9b91296fd9ab492144e043c6193ac564","schema_version":"1.0","event_id":"sha256:f93e99d3946e70cfb19e2e698591abbb9b91296fd9ab492144e043c6193ac564"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3LZN2QRDO4MXBQU76CLN7KWT6F/bundle.json","state_url":"https://pith.science/pith/3LZN2QRDO4MXBQU76CLN7KWT6F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3LZN2QRDO4MXBQU76CLN7KWT6F/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":"2026-05-28T03:30:28Z","links":{"resolver":"https://pith.science/pith/3LZN2QRDO4MXBQU76CLN7KWT6F","bundle":"https://pith.science/pith/3LZN2QRDO4MXBQU76CLN7KWT6F/bundle.json","state":"https://pith.science/pith/3LZN2QRDO4MXBQU76CLN7KWT6F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3LZN2QRDO4MXBQU76CLN7KWT6F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3LZN2QRDO4MXBQU76CLN7KWT6F","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":"a2ae8e4b555bd7e9c5360db70d20d8d111bec39c75dc4c32c624f67dca4a7275","cross_cats_sorted":["gr-qc","hep-th","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-07-22T18:56:18Z","title_canon_sha256":"934362b4a5a05c54122a3b2066a5bd7d883cd3c5b7337ec6d02ed9fdae32e561"},"schema_version":"1.0","source":{"id":"1407.5972","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.5972","created_at":"2026-05-18T01:42:33Z"},{"alias_kind":"arxiv_version","alias_value":"1407.5972v2","created_at":"2026-05-18T01:42:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5972","created_at":"2026-05-18T01:42:33Z"},{"alias_kind":"pith_short_12","alias_value":"3LZN2QRDO4MX","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3LZN2QRDO4MXBQU7","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3LZN2QRD","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:f93e99d3946e70cfb19e2e698591abbb9b91296fd9ab492144e043c6193ac564","target":"graph","created_at":"2026-05-18T01:42:33Z","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 use pseudodifferential calculus and heat kernel techniques to prove a conjecture by Chamseddine and Connes on rationality of the coefficients of the polynomials in the cosmic scale factor $a(t)$ and its higher derivatives, which describe the general terms $a_{2n}$ in the expansion of the spectral action for general Robertson-Walker metrics. We also compute the terms up to $a_{12}$ in the expansion of the spectral action by our method. As a byproduct, we verify that our computations agree with the terms up to $a_{10}$ that were previously computed by Chamseddine and Connes by a different met","authors_text":"Asghar Ghorbanpour, Farzad Fathizadeh, Masoud Khalkhali","cross_cats":["gr-qc","hep-th","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-07-22T18:56:18Z","title":"Rationality of Spectral Action for Robertson-Walker Metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5972","kind":"arxiv","version":2},"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":"sha256:3728d2e39e09a79eea9be581aa356ff3b4f7be09316dc5e353b12bb61a4349aa","target":"record","created_at":"2026-05-18T01:42:33Z","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":"a2ae8e4b555bd7e9c5360db70d20d8d111bec39c75dc4c32c624f67dca4a7275","cross_cats_sorted":["gr-qc","hep-th","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-07-22T18:56:18Z","title_canon_sha256":"934362b4a5a05c54122a3b2066a5bd7d883cd3c5b7337ec6d02ed9fdae32e561"},"schema_version":"1.0","source":{"id":"1407.5972","kind":"arxiv","version":2}},"canonical_sha256":"daf2dd4223771970c29ff096dfaad3f16d7f6b8c606f504176ecb5c98134c14c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"daf2dd4223771970c29ff096dfaad3f16d7f6b8c606f504176ecb5c98134c14c","first_computed_at":"2026-05-18T01:42:33.004285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:42:33.004285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zkCo6AzlrI2uq4t0rTGqYhF57rjtrYfgYSI25IeU7G8u48x/NB7VZbBrK7cypnhGARnyhDU4WIhEcJY2gefiCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:42:33.004756Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.5972","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3728d2e39e09a79eea9be581aa356ff3b4f7be09316dc5e353b12bb61a4349aa","sha256:f93e99d3946e70cfb19e2e698591abbb9b91296fd9ab492144e043c6193ac564"],"state_sha256":"21d75cf706b7dd50fe025737f2dd80a172e6b8b945e5499349e59e81923bb59b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1r9EKu1J36UEI9FQP/zv3ExyAOD3lJI28GlSdZ+AOz8cIoFRGGlpLS36Mqu2k+AecnMftjhXnHq44AZrGuG6Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T03:30:28.243610Z","bundle_sha256":"89509f5ea93f0beaac361fcb49efeb1c1ce4e88d1871d4c37e902f562d4fee94"}}