{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:65SKYGSATFBMERAOXPKNHFGZVO","short_pith_number":"pith:65SKYGSA","canonical_record":{"source":{"id":"1603.04289","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2016-03-14T14:54:30Z","cross_cats_sorted":["math-ph","math.MP","math.NT"],"title_canon_sha256":"1fe80af2d1344294d3ff1fa2ffbd8aaaf667392cf2b6d2daa5758541cda842e7","abstract_canon_sha256":"3e1fcd89b77a695b92b41d463a3f35dfa24a7af24c8171edf0778ace2ed9122e"},"schema_version":"1.0"},"canonical_sha256":"f764ac1a409942c2440ebbd4d394d9ab8dbad0ef3aaf6cdf45899fc9b942e13e","source":{"kind":"arxiv","id":"1603.04289","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04289","created_at":"2026-05-18T00:27:10Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04289v2","created_at":"2026-05-18T00:27:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04289","created_at":"2026-05-18T00:27:10Z"},{"alias_kind":"pith_short_12","alias_value":"65SKYGSATFBM","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"65SKYGSATFBMERAO","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"65SKYGSA","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:65SKYGSATFBMERAOXPKNHFGZVO","target":"record","payload":{"canonical_record":{"source":{"id":"1603.04289","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2016-03-14T14:54:30Z","cross_cats_sorted":["math-ph","math.MP","math.NT"],"title_canon_sha256":"1fe80af2d1344294d3ff1fa2ffbd8aaaf667392cf2b6d2daa5758541cda842e7","abstract_canon_sha256":"3e1fcd89b77a695b92b41d463a3f35dfa24a7af24c8171edf0778ace2ed9122e"},"schema_version":"1.0"},"canonical_sha256":"f764ac1a409942c2440ebbd4d394d9ab8dbad0ef3aaf6cdf45899fc9b942e13e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:10.123274Z","signature_b64":"fGg3jF4uxgL/yjLy1mw5S4BXaZir0wn0a0r2i1k+26hsh/pZvZDbgd9SgN6qOdCDiOl7yJ7z0F30pFsMuDDjDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f764ac1a409942c2440ebbd4d394d9ab8dbad0ef3aaf6cdf45899fc9b942e13e","last_reissued_at":"2026-05-18T00:27:10.122668Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:10.122668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.04289","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":"2026-05-18T00:27:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xq5d5kwFNAEqzolw6Vk0DMXdFJ5KNLWADgfa0covaiGXlPkrCDEnMatBPRzP/IynrQ7i+lkII+TwUSB9+v4rBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T13:08:03.709944Z"},"content_sha256":"9e6538d866baf8415b644d07c1cfa51ee4c80ba3a36dbed5fb2af991c0b5582b","schema_version":"1.0","event_id":"sha256:9e6538d866baf8415b644d07c1cfa51ee4c80ba3a36dbed5fb2af991c0b5582b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:65SKYGSATFBMERAOXPKNHFGZVO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Galois coaction on $\\phi^4$ periods","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","math.NT"],"primary_cat":"hep-th","authors_text":"Erik Panzer, Oliver Schnetz","submitted_at":"2016-03-14T14:54:30Z","abstract_excerpt":"We report on calculations of Feynman periods of primitive log-divergent $\\phi^4$ graphs up to eleven loops. The structure of $\\phi^4$ periods is described by a series of conjectures. In particular, we discuss the possibility that $\\phi^4$ periods are a comodule under the Galois coaction. Finally, we compare the results with the periods of primitive log-divergent non-$\\phi^4$ graphs up to eight loops and find remarkable differences to $\\phi^4$ periods. Explicit results for all periods we could compute are provided in ancillary files."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04289","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":"2026-05-18T00:27:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"crNHQd83AebaJYWfLWglbuQ2Pq0mhLvS5+06TRnNA7w95fAaWlj0MN9rb72aVyxa9Fm9g/f382m/t+TUSITmCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T13:08:03.710647Z"},"content_sha256":"c24c56a951199b23fa2eb923b1e5c97a6a62313aa93941015ce81004583110e6","schema_version":"1.0","event_id":"sha256:c24c56a951199b23fa2eb923b1e5c97a6a62313aa93941015ce81004583110e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/65SKYGSATFBMERAOXPKNHFGZVO/bundle.json","state_url":"https://pith.science/pith/65SKYGSATFBMERAOXPKNHFGZVO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/65SKYGSATFBMERAOXPKNHFGZVO/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":"2026-08-06T13:08:03Z","links":{"resolver":"https://pith.science/pith/65SKYGSATFBMERAOXPKNHFGZVO","bundle":"https://pith.science/pith/65SKYGSATFBMERAOXPKNHFGZVO/bundle.json","state":"https://pith.science/pith/65SKYGSATFBMERAOXPKNHFGZVO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/65SKYGSATFBMERAOXPKNHFGZVO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:65SKYGSATFBMERAOXPKNHFGZVO","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":"3e1fcd89b77a695b92b41d463a3f35dfa24a7af24c8171edf0778ace2ed9122e","cross_cats_sorted":["math-ph","math.MP","math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2016-03-14T14:54:30Z","title_canon_sha256":"1fe80af2d1344294d3ff1fa2ffbd8aaaf667392cf2b6d2daa5758541cda842e7"},"schema_version":"1.0","source":{"id":"1603.04289","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04289","created_at":"2026-05-18T00:27:10Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04289v2","created_at":"2026-05-18T00:27:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04289","created_at":"2026-05-18T00:27:10Z"},{"alias_kind":"pith_short_12","alias_value":"65SKYGSATFBM","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"65SKYGSATFBMERAO","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"65SKYGSA","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:c24c56a951199b23fa2eb923b1e5c97a6a62313aa93941015ce81004583110e6","target":"graph","created_at":"2026-05-18T00:27:10Z","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 report on calculations of Feynman periods of primitive log-divergent $\\phi^4$ graphs up to eleven loops. The structure of $\\phi^4$ periods is described by a series of conjectures. In particular, we discuss the possibility that $\\phi^4$ periods are a comodule under the Galois coaction. Finally, we compare the results with the periods of primitive log-divergent non-$\\phi^4$ graphs up to eight loops and find remarkable differences to $\\phi^4$ periods. Explicit results for all periods we could compute are provided in ancillary files.","authors_text":"Erik Panzer, Oliver Schnetz","cross_cats":["math-ph","math.MP","math.NT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2016-03-14T14:54:30Z","title":"The Galois coaction on $\\phi^4$ periods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04289","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":"sha256:9e6538d866baf8415b644d07c1cfa51ee4c80ba3a36dbed5fb2af991c0b5582b","target":"record","created_at":"2026-05-18T00:27:10Z","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":"3e1fcd89b77a695b92b41d463a3f35dfa24a7af24c8171edf0778ace2ed9122e","cross_cats_sorted":["math-ph","math.MP","math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2016-03-14T14:54:30Z","title_canon_sha256":"1fe80af2d1344294d3ff1fa2ffbd8aaaf667392cf2b6d2daa5758541cda842e7"},"schema_version":"1.0","source":{"id":"1603.04289","kind":"arxiv","version":2}},"canonical_sha256":"f764ac1a409942c2440ebbd4d394d9ab8dbad0ef3aaf6cdf45899fc9b942e13e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f764ac1a409942c2440ebbd4d394d9ab8dbad0ef3aaf6cdf45899fc9b942e13e","first_computed_at":"2026-05-18T00:27:10.122668Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:10.122668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fGg3jF4uxgL/yjLy1mw5S4BXaZir0wn0a0r2i1k+26hsh/pZvZDbgd9SgN6qOdCDiOl7yJ7z0F30pFsMuDDjDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:10.123274Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.04289","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e6538d866baf8415b644d07c1cfa51ee4c80ba3a36dbed5fb2af991c0b5582b","sha256:c24c56a951199b23fa2eb923b1e5c97a6a62313aa93941015ce81004583110e6"],"state_sha256":"db1983df7340361c80b59ca78f9784e5c87f5afb54bef573bbbb01ff26a4a66d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gq7I8qHUlRvDqIZBTzMPcmpN+alV/9S2QC+XDuAirTWDgPnP/QCxaUgppldRdBIUX2OPuyxk5uqYjgaOT54SCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T13:08:03.716622Z","bundle_sha256":"f56dc2851ff35e49d0450b7cf8fd64de6eb1733df2cbef8ef41b7bcd469dbb05"}}