{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:XXSSSQWLBMNJLQ7QTN6IRBYLWE","short_pith_number":"pith:XXSSSQWL","canonical_record":{"source":{"id":"2509.02684","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-09-02T18:00:03Z","cross_cats_sorted":["astro-ph.CO","hep-ph"],"title_canon_sha256":"0ca72b02a73a1979db967e12c87acd88063182c9e085b3f9bea2e1b02dca456d","abstract_canon_sha256":"4e6ff1631c404f34b99dff200ebc3fa22203d2af1f6cf6803bf0e228df65e23b"},"schema_version":"1.0"},"canonical_sha256":"bde52942cb0b1a95c3f09b7c88870bb110fcd9f6389b08ae3f97f215ede5b53b","source":{"kind":"arxiv","id":"2509.02684","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.02684","created_at":"2026-07-05T12:03:55Z"},{"alias_kind":"arxiv_version","alias_value":"2509.02684v1","created_at":"2026-07-05T12:03:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.02684","created_at":"2026-07-05T12:03:55Z"},{"alias_kind":"pith_short_12","alias_value":"XXSSSQWLBMNJ","created_at":"2026-07-05T12:03:55Z"},{"alias_kind":"pith_short_16","alias_value":"XXSSSQWLBMNJLQ7Q","created_at":"2026-07-05T12:03:55Z"},{"alias_kind":"pith_short_8","alias_value":"XXSSSQWL","created_at":"2026-07-05T12:03:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:XXSSSQWLBMNJLQ7QTN6IRBYLWE","target":"record","payload":{"canonical_record":{"source":{"id":"2509.02684","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-09-02T18:00:03Z","cross_cats_sorted":["astro-ph.CO","hep-ph"],"title_canon_sha256":"0ca72b02a73a1979db967e12c87acd88063182c9e085b3f9bea2e1b02dca456d","abstract_canon_sha256":"4e6ff1631c404f34b99dff200ebc3fa22203d2af1f6cf6803bf0e228df65e23b"},"schema_version":"1.0"},"canonical_sha256":"bde52942cb0b1a95c3f09b7c88870bb110fcd9f6389b08ae3f97f215ede5b53b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:03:55.592710Z","signature_b64":"bq5LCQp73hHovMMeI4s1Ei3S067FMTCKfO/EAjUgOe3XM8ISlMAJufUQR1juXfq5VIXx3VzU4yVimNX+6JCoBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bde52942cb0b1a95c3f09b7c88870bb110fcd9f6389b08ae3f97f215ede5b53b","last_reissued_at":"2026-07-05T12:03:55.591927Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:03:55.591927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.02684","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":"2026-07-05T12:03:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wGh/2Tw31eureDKntKNQhGUseaNh7SowmzjcZJZvK7D9mltjMBL8ttzkVViITlvwrPa7EQpSW40wF+wjRGDVCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T17:56:35.939767Z"},"content_sha256":"a97fdba09e25dc21560287fa071df66ff462a0fbbe699abfe878e0a13edfd0b7","schema_version":"1.0","event_id":"sha256:a97fdba09e25dc21560287fa071df66ff462a0fbbe699abfe878e0a13edfd0b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:XXSSSQWLBMNJLQ7QTN6IRBYLWE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Anatomy of Family Trees in Cosmological Correlators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["astro-ph.CO","hep-ph"],"primary_cat":"hep-th","authors_text":"Bingchu Fan, Zhong-Zhi Xianyu","submitted_at":"2025-09-02T18:00:03Z","abstract_excerpt":"The time-ordered multilayer integrals have long been cited as major challenges in the analytical study of cosmological correlators and wavefunction coefficients. The recently proposed family tree decomposition technique solved these time integrals in terms of canonical objects called family trees, which are multivariate hypergeometric functions with energies as variables and twists as parameters. In this work, we provide a systematic study of the analytical properties of family trees. By exploiting the great flexibility of Mellin representations of family trees, we identify and characterize al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.02684","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.02684/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":"2026-07-05T12:03:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ejga3vADX5aW8x4qMLzIdbMsUnLjMZHM5zdrBVSBNl7JaXxgt4cw5Lesko3hcUq9GeUBlYHBCg2TIJWRMsEBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T17:56:35.940400Z"},"content_sha256":"4ee09cb183bc78e8ddea402100702e8a0fca626786ee5564df1a346385f23ebf","schema_version":"1.0","event_id":"sha256:4ee09cb183bc78e8ddea402100702e8a0fca626786ee5564df1a346385f23ebf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XXSSSQWLBMNJLQ7QTN6IRBYLWE/bundle.json","state_url":"https://pith.science/pith/XXSSSQWLBMNJLQ7QTN6IRBYLWE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XXSSSQWLBMNJLQ7QTN6IRBYLWE/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":"2026-08-19T17:56:35Z","links":{"resolver":"https://pith.science/pith/XXSSSQWLBMNJLQ7QTN6IRBYLWE","bundle":"https://pith.science/pith/XXSSSQWLBMNJLQ7QTN6IRBYLWE/bundle.json","state":"https://pith.science/pith/XXSSSQWLBMNJLQ7QTN6IRBYLWE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XXSSSQWLBMNJLQ7QTN6IRBYLWE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:XXSSSQWLBMNJLQ7QTN6IRBYLWE","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":"4e6ff1631c404f34b99dff200ebc3fa22203d2af1f6cf6803bf0e228df65e23b","cross_cats_sorted":["astro-ph.CO","hep-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-09-02T18:00:03Z","title_canon_sha256":"0ca72b02a73a1979db967e12c87acd88063182c9e085b3f9bea2e1b02dca456d"},"schema_version":"1.0","source":{"id":"2509.02684","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.02684","created_at":"2026-07-05T12:03:55Z"},{"alias_kind":"arxiv_version","alias_value":"2509.02684v1","created_at":"2026-07-05T12:03:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.02684","created_at":"2026-07-05T12:03:55Z"},{"alias_kind":"pith_short_12","alias_value":"XXSSSQWLBMNJ","created_at":"2026-07-05T12:03:55Z"},{"alias_kind":"pith_short_16","alias_value":"XXSSSQWLBMNJLQ7Q","created_at":"2026-07-05T12:03:55Z"},{"alias_kind":"pith_short_8","alias_value":"XXSSSQWL","created_at":"2026-07-05T12:03:55Z"}],"graph_snapshots":[{"event_id":"sha256:4ee09cb183bc78e8ddea402100702e8a0fca626786ee5564df1a346385f23ebf","target":"graph","created_at":"2026-07-05T12:03:55Z","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/2509.02684/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The time-ordered multilayer integrals have long been cited as major challenges in the analytical study of cosmological correlators and wavefunction coefficients. The recently proposed family tree decomposition technique solved these time integrals in terms of canonical objects called family trees, which are multivariate hypergeometric functions with energies as variables and twists as parameters. In this work, we provide a systematic study of the analytical properties of family trees. By exploiting the great flexibility of Mellin representations of family trees, we identify and characterize al","authors_text":"Bingchu Fan, Zhong-Zhi Xianyu","cross_cats":["astro-ph.CO","hep-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-09-02T18:00:03Z","title":"Anatomy of Family Trees in Cosmological Correlators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.02684","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:a97fdba09e25dc21560287fa071df66ff462a0fbbe699abfe878e0a13edfd0b7","target":"record","created_at":"2026-07-05T12:03:55Z","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":"4e6ff1631c404f34b99dff200ebc3fa22203d2af1f6cf6803bf0e228df65e23b","cross_cats_sorted":["astro-ph.CO","hep-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-09-02T18:00:03Z","title_canon_sha256":"0ca72b02a73a1979db967e12c87acd88063182c9e085b3f9bea2e1b02dca456d"},"schema_version":"1.0","source":{"id":"2509.02684","kind":"arxiv","version":1}},"canonical_sha256":"bde52942cb0b1a95c3f09b7c88870bb110fcd9f6389b08ae3f97f215ede5b53b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bde52942cb0b1a95c3f09b7c88870bb110fcd9f6389b08ae3f97f215ede5b53b","first_computed_at":"2026-07-05T12:03:55.591927Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:03:55.591927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bq5LCQp73hHovMMeI4s1Ei3S067FMTCKfO/EAjUgOe3XM8ISlMAJufUQR1juXfq5VIXx3VzU4yVimNX+6JCoBg==","signature_status":"signed_v1","signed_at":"2026-07-05T12:03:55.592710Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.02684","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a97fdba09e25dc21560287fa071df66ff462a0fbbe699abfe878e0a13edfd0b7","sha256:4ee09cb183bc78e8ddea402100702e8a0fca626786ee5564df1a346385f23ebf"],"state_sha256":"0662ec986dfb5045da760213c006824d09af2146e13e8342856bd36e42ad02a6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2D2yBis4zRnnQgv9xY08vBnJoVBep2EkxFw2RS61BCCrvis71e14YGJxrGS0faptcvXcWlLIJ3uIMg/ihUeMCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T17:56:35.947215Z","bundle_sha256":"d0946b059d11e62c9d6c9fc2fff06d83953aa343aef0c04a18ff0a14f2057fa0"}}