{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ILJYVRRWVBVAGC62YV6XCMYF3Z","short_pith_number":"pith:ILJYVRRW","canonical_record":{"source":{"id":"1207.6404","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-07-26T20:08:16Z","cross_cats_sorted":["math-ph","math.CT","math.MP"],"title_canon_sha256":"7c0b43abb8b1648107acd1789f625dc05ef38ca65aa29d6b8bfa50fbf8d7f529","abstract_canon_sha256":"fd158b3d756438625b9c61d227b564215f2b3768e4701c0e2614421c540f825d"},"schema_version":"1.0"},"canonical_sha256":"42d38ac636a86a030bdac57d713305de6a0428434da880a31561f6b9ca19d965","source":{"kind":"arxiv","id":"1207.6404","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.6404","created_at":"2026-05-18T02:52:56Z"},{"alias_kind":"arxiv_version","alias_value":"1207.6404v2","created_at":"2026-05-18T02:52:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6404","created_at":"2026-05-18T02:52:56Z"},{"alias_kind":"pith_short_12","alias_value":"ILJYVRRWVBVA","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"ILJYVRRWVBVAGC62","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"ILJYVRRW","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ILJYVRRWVBVAGC62YV6XCMYF3Z","target":"record","payload":{"canonical_record":{"source":{"id":"1207.6404","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-07-26T20:08:16Z","cross_cats_sorted":["math-ph","math.CT","math.MP"],"title_canon_sha256":"7c0b43abb8b1648107acd1789f625dc05ef38ca65aa29d6b8bfa50fbf8d7f529","abstract_canon_sha256":"fd158b3d756438625b9c61d227b564215f2b3768e4701c0e2614421c540f825d"},"schema_version":"1.0"},"canonical_sha256":"42d38ac636a86a030bdac57d713305de6a0428434da880a31561f6b9ca19d965","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:56.324024Z","signature_b64":"l522c1jiMFZFopgWqyGPkNM1AVZeFp0x83vwIDtNNSijbQ6SJhdq3UpkGSV1r+RuVCzOUYvtxaeSh3mxBtwjAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42d38ac636a86a030bdac57d713305de6a0428434da880a31561f6b9ca19d965","last_reissued_at":"2026-05-18T02:52:56.323377Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:56.323377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.6404","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":"2026-05-18T02:52:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zkus8oBHtv4tj0DUoulFHkiyPFWeT6KHfor7ZRpumcJK7lw6D9Bu95upadSKC1KI89hScbat0M4rABuvKhmoCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:22:34.706739Z"},"content_sha256":"ea58f21c0bc5b786b5cf6cf5d66360a38e154b4acbd03a191fe705ac7cd02936","schema_version":"1.0","event_id":"sha256:ea58f21c0bc5b786b5cf6cf5d66360a38e154b4acbd03a191fe705ac7cd02936"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ILJYVRRWVBVAGC62YV6XCMYF3Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Groupoids and Faa di Bruno formulae for Green functions in bialgebras of trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CT","math.MP"],"primary_cat":"math.QA","authors_text":"Andrew Tonks, Imma Galvez-Carrillo, Joachim Kock","submitted_at":"2012-07-26T20:08:16Z","abstract_excerpt":"We prove a Faa di Bruno formula for the Green function in the bialgebra of P-trees, for any polynomial endofunctor P. The formula appears as relative homotopy cardinality of an equivalence of groupoids."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6404","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":"2026-05-18T02:52:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tdkOy87HzxJ52jGjGL5lJLjeRzcqLxB2jVs8imegZ4CMSoqV9czjvTx9C6nIAVoBBms9zXwDpsAau5jPS1p1Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:22:34.707090Z"},"content_sha256":"4fa88a137a11579c15c851c2eb45ee849d2b6c0f4da204fe2e9b538598e6196c","schema_version":"1.0","event_id":"sha256:4fa88a137a11579c15c851c2eb45ee849d2b6c0f4da204fe2e9b538598e6196c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ILJYVRRWVBVAGC62YV6XCMYF3Z/bundle.json","state_url":"https://pith.science/pith/ILJYVRRWVBVAGC62YV6XCMYF3Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ILJYVRRWVBVAGC62YV6XCMYF3Z/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":"2026-06-22T10:22:34Z","links":{"resolver":"https://pith.science/pith/ILJYVRRWVBVAGC62YV6XCMYF3Z","bundle":"https://pith.science/pith/ILJYVRRWVBVAGC62YV6XCMYF3Z/bundle.json","state":"https://pith.science/pith/ILJYVRRWVBVAGC62YV6XCMYF3Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ILJYVRRWVBVAGC62YV6XCMYF3Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ILJYVRRWVBVAGC62YV6XCMYF3Z","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":"fd158b3d756438625b9c61d227b564215f2b3768e4701c0e2614421c540f825d","cross_cats_sorted":["math-ph","math.CT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-07-26T20:08:16Z","title_canon_sha256":"7c0b43abb8b1648107acd1789f625dc05ef38ca65aa29d6b8bfa50fbf8d7f529"},"schema_version":"1.0","source":{"id":"1207.6404","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.6404","created_at":"2026-05-18T02:52:56Z"},{"alias_kind":"arxiv_version","alias_value":"1207.6404v2","created_at":"2026-05-18T02:52:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6404","created_at":"2026-05-18T02:52:56Z"},{"alias_kind":"pith_short_12","alias_value":"ILJYVRRWVBVA","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"ILJYVRRWVBVAGC62","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"ILJYVRRW","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:4fa88a137a11579c15c851c2eb45ee849d2b6c0f4da204fe2e9b538598e6196c","target":"graph","created_at":"2026-05-18T02:52:56Z","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 prove a Faa di Bruno formula for the Green function in the bialgebra of P-trees, for any polynomial endofunctor P. The formula appears as relative homotopy cardinality of an equivalence of groupoids.","authors_text":"Andrew Tonks, Imma Galvez-Carrillo, Joachim Kock","cross_cats":["math-ph","math.CT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-07-26T20:08:16Z","title":"Groupoids and Faa di Bruno formulae for Green functions in bialgebras of trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6404","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:ea58f21c0bc5b786b5cf6cf5d66360a38e154b4acbd03a191fe705ac7cd02936","target":"record","created_at":"2026-05-18T02:52:56Z","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":"fd158b3d756438625b9c61d227b564215f2b3768e4701c0e2614421c540f825d","cross_cats_sorted":["math-ph","math.CT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-07-26T20:08:16Z","title_canon_sha256":"7c0b43abb8b1648107acd1789f625dc05ef38ca65aa29d6b8bfa50fbf8d7f529"},"schema_version":"1.0","source":{"id":"1207.6404","kind":"arxiv","version":2}},"canonical_sha256":"42d38ac636a86a030bdac57d713305de6a0428434da880a31561f6b9ca19d965","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42d38ac636a86a030bdac57d713305de6a0428434da880a31561f6b9ca19d965","first_computed_at":"2026-05-18T02:52:56.323377Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:56.323377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l522c1jiMFZFopgWqyGPkNM1AVZeFp0x83vwIDtNNSijbQ6SJhdq3UpkGSV1r+RuVCzOUYvtxaeSh3mxBtwjAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:56.324024Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.6404","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea58f21c0bc5b786b5cf6cf5d66360a38e154b4acbd03a191fe705ac7cd02936","sha256:4fa88a137a11579c15c851c2eb45ee849d2b6c0f4da204fe2e9b538598e6196c"],"state_sha256":"efba08f921d6170b0e3c2ecec33fa8d8bd20b4a66bf7f84d4473b41688806383"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3C5GqU5Yp0LG4nM2yODdUdAoFWj997ThUWU9Vlj1rdCa3HjQJDXS62k3neFVFF24nyB47RQhpp9HNJ1gzdO5DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T10:22:34.709105Z","bundle_sha256":"59bb7d31aedfd45e4b58d62d57a8e100f5b55b585061cb4b53b2e10c4c84b347"}}