{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:EUPK3EUSD7EANXL7EK34EQ4RHN","short_pith_number":"pith:EUPK3EUS","canonical_record":{"source":{"id":"1904.11231","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-04-25T09:32:20Z","cross_cats_sorted":["math.CO","math.MP"],"title_canon_sha256":"44fc2fe1a4924af349712c7fd1604eca3871f395955b1a8b858e59fadbff9174","abstract_canon_sha256":"a6590f2f36d6e6a90c2fb7a9174786b9baa000df58a27edebd6364a3081b8151"},"schema_version":"1.0"},"canonical_sha256":"251ead92921fc806dd7f22b7c243913b4421ef04f18b6ee51663e4cf987cb28f","source":{"kind":"arxiv","id":"1904.11231","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.11231","created_at":"2026-07-05T04:14:35Z"},{"alias_kind":"arxiv_version","alias_value":"1904.11231v2","created_at":"2026-07-05T04:14:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.11231","created_at":"2026-07-05T04:14:35Z"},{"alias_kind":"pith_short_12","alias_value":"EUPK3EUSD7EA","created_at":"2026-07-05T04:14:35Z"},{"alias_kind":"pith_short_16","alias_value":"EUPK3EUSD7EANXL7","created_at":"2026-07-05T04:14:35Z"},{"alias_kind":"pith_short_8","alias_value":"EUPK3EUS","created_at":"2026-07-05T04:14:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:EUPK3EUSD7EANXL7EK34EQ4RHN","target":"record","payload":{"canonical_record":{"source":{"id":"1904.11231","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-04-25T09:32:20Z","cross_cats_sorted":["math.CO","math.MP"],"title_canon_sha256":"44fc2fe1a4924af349712c7fd1604eca3871f395955b1a8b858e59fadbff9174","abstract_canon_sha256":"a6590f2f36d6e6a90c2fb7a9174786b9baa000df58a27edebd6364a3081b8151"},"schema_version":"1.0"},"canonical_sha256":"251ead92921fc806dd7f22b7c243913b4421ef04f18b6ee51663e4cf987cb28f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:14:35.451894Z","signature_b64":"Suf9SQ9jFP6iQbEzV4rjdGnoYqBAb+jcp9cuuuvL4BSGhUFOb8m5IAxUVKhyHFG71vqPGn+Yx0ApOoT7AGh2BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"251ead92921fc806dd7f22b7c243913b4421ef04f18b6ee51663e4cf987cb28f","last_reissued_at":"2026-07-05T04:14:35.451404Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:14:35.451404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.11231","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":"2026-07-05T04:14:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GPVFfYfHvOQunxT2h+9bed+QCFRzcqJgUS+TT277VKNQCGa+7z0j4hMHu6Nz8v3mQlXyBkE+P3bWHee78aHMAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T03:39:03.854834Z"},"content_sha256":"bae4090a8d8e70d9c061279785ff82f113ec08965c0bc27a57a1bb4bdce8b14b","schema_version":"1.0","event_id":"sha256:bae4090a8d8e70d9c061279785ff82f113ec08965c0bc27a57a1bb4bdce8b14b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:EUPK3EUSD7EANXL7EK34EQ4RHN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nested Catalan tables and a recurrence relation in noncommutative quantum field theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MP"],"primary_cat":"math-ph","authors_text":"Alexander Hock, Jins de Jong, Raimar Wulkenhaar (M\\\"unster)","submitted_at":"2019-04-25T09:32:20Z","abstract_excerpt":"Correlation functions in a dynamic quartic matrix model are obtained from the two-point function through a recurrence relation. This paper gives the explicit solution of the recurrence by mapping it bijectively to a two-fold nested combinatorial structure each counted by Catalan numbers. These `nested Catalan tables' have a description as diagrams of non-crossing chords and threads."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.11231","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1904.11231/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":"2026-07-05T04:14:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VB9RSc3R0+2z3nRjksY03/VkCPRNbm1bumIo1ibEZH1TMXwmEGQ3Cv1bjf+nTpZX8lqSsj3sv0LkQqVWMMXJCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T03:39:03.855209Z"},"content_sha256":"1d10529e243f238f153483e0a32640a1c2c73b299cf437428a103988233b68a6","schema_version":"1.0","event_id":"sha256:1d10529e243f238f153483e0a32640a1c2c73b299cf437428a103988233b68a6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EUPK3EUSD7EANXL7EK34EQ4RHN/bundle.json","state_url":"https://pith.science/pith/EUPK3EUSD7EANXL7EK34EQ4RHN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EUPK3EUSD7EANXL7EK34EQ4RHN/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":"2026-08-23T03:39:03Z","links":{"resolver":"https://pith.science/pith/EUPK3EUSD7EANXL7EK34EQ4RHN","bundle":"https://pith.science/pith/EUPK3EUSD7EANXL7EK34EQ4RHN/bundle.json","state":"https://pith.science/pith/EUPK3EUSD7EANXL7EK34EQ4RHN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EUPK3EUSD7EANXL7EK34EQ4RHN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:EUPK3EUSD7EANXL7EK34EQ4RHN","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":"a6590f2f36d6e6a90c2fb7a9174786b9baa000df58a27edebd6364a3081b8151","cross_cats_sorted":["math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-04-25T09:32:20Z","title_canon_sha256":"44fc2fe1a4924af349712c7fd1604eca3871f395955b1a8b858e59fadbff9174"},"schema_version":"1.0","source":{"id":"1904.11231","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.11231","created_at":"2026-07-05T04:14:35Z"},{"alias_kind":"arxiv_version","alias_value":"1904.11231v2","created_at":"2026-07-05T04:14:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.11231","created_at":"2026-07-05T04:14:35Z"},{"alias_kind":"pith_short_12","alias_value":"EUPK3EUSD7EA","created_at":"2026-07-05T04:14:35Z"},{"alias_kind":"pith_short_16","alias_value":"EUPK3EUSD7EANXL7","created_at":"2026-07-05T04:14:35Z"},{"alias_kind":"pith_short_8","alias_value":"EUPK3EUS","created_at":"2026-07-05T04:14:35Z"}],"graph_snapshots":[{"event_id":"sha256:1d10529e243f238f153483e0a32640a1c2c73b299cf437428a103988233b68a6","target":"graph","created_at":"2026-07-05T04:14:35Z","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/1904.11231/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Correlation functions in a dynamic quartic matrix model are obtained from the two-point function through a recurrence relation. This paper gives the explicit solution of the recurrence by mapping it bijectively to a two-fold nested combinatorial structure each counted by Catalan numbers. These `nested Catalan tables' have a description as diagrams of non-crossing chords and threads.","authors_text":"Alexander Hock, Jins de Jong, Raimar Wulkenhaar (M\\\"unster)","cross_cats":["math.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-04-25T09:32:20Z","title":"Nested Catalan tables and a recurrence relation in noncommutative quantum field theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.11231","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:bae4090a8d8e70d9c061279785ff82f113ec08965c0bc27a57a1bb4bdce8b14b","target":"record","created_at":"2026-07-05T04:14:35Z","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":"a6590f2f36d6e6a90c2fb7a9174786b9baa000df58a27edebd6364a3081b8151","cross_cats_sorted":["math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-04-25T09:32:20Z","title_canon_sha256":"44fc2fe1a4924af349712c7fd1604eca3871f395955b1a8b858e59fadbff9174"},"schema_version":"1.0","source":{"id":"1904.11231","kind":"arxiv","version":2}},"canonical_sha256":"251ead92921fc806dd7f22b7c243913b4421ef04f18b6ee51663e4cf987cb28f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"251ead92921fc806dd7f22b7c243913b4421ef04f18b6ee51663e4cf987cb28f","first_computed_at":"2026-07-05T04:14:35.451404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:14:35.451404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Suf9SQ9jFP6iQbEzV4rjdGnoYqBAb+jcp9cuuuvL4BSGhUFOb8m5IAxUVKhyHFG71vqPGn+Yx0ApOoT7AGh2BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:14:35.451894Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.11231","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bae4090a8d8e70d9c061279785ff82f113ec08965c0bc27a57a1bb4bdce8b14b","sha256:1d10529e243f238f153483e0a32640a1c2c73b299cf437428a103988233b68a6"],"state_sha256":"2d0353d49cd89eb5700c2704c42f0b67bdf576054ebbd74ca01ee9d1be1f31b5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"//+8u2tJtJ1znzpt/WizCX1ctJDayD1C8vnUOIEBBrH9CdAYhldSBFH5PJED2dh+BkZOly8PoQbY9wqn2+byAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T03:39:03.857836Z","bundle_sha256":"50d6fc64ff36a822dfe0a76d3d5769182778dcd401606fb470d4698b589ef230"}}