{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:G2ZSV37SJ6HEHJ4Z3QRO67Z2OA","short_pith_number":"pith:G2ZSV37S","canonical_record":{"source":{"id":"2307.03044","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2023-07-06T15:09:44Z","cross_cats_sorted":["math.CT","math.RA"],"title_canon_sha256":"3181f6ede0c3ef7873f61d03ea300d35d542354f09a0a5c2203e97626bdba584","abstract_canon_sha256":"760696285bdab6877769dd14d12a62ec36aa8236d328faa8114f7e8b2ef41ee3"},"schema_version":"1.0"},"canonical_sha256":"36b32aeff24f8e43a799dc22ef7f3a703b15389616a1c3af8befcc9b7c78ab57","source":{"kind":"arxiv","id":"2307.03044","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.03044","created_at":"2026-07-05T07:10:49Z"},{"alias_kind":"arxiv_version","alias_value":"2307.03044v2","created_at":"2026-07-05T07:10:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.03044","created_at":"2026-07-05T07:10:49Z"},{"alias_kind":"pith_short_12","alias_value":"G2ZSV37SJ6HE","created_at":"2026-07-05T07:10:49Z"},{"alias_kind":"pith_short_16","alias_value":"G2ZSV37SJ6HEHJ4Z","created_at":"2026-07-05T07:10:49Z"},{"alias_kind":"pith_short_8","alias_value":"G2ZSV37S","created_at":"2026-07-05T07:10:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:G2ZSV37SJ6HEHJ4Z3QRO67Z2OA","target":"record","payload":{"canonical_record":{"source":{"id":"2307.03044","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2023-07-06T15:09:44Z","cross_cats_sorted":["math.CT","math.RA"],"title_canon_sha256":"3181f6ede0c3ef7873f61d03ea300d35d542354f09a0a5c2203e97626bdba584","abstract_canon_sha256":"760696285bdab6877769dd14d12a62ec36aa8236d328faa8114f7e8b2ef41ee3"},"schema_version":"1.0"},"canonical_sha256":"36b32aeff24f8e43a799dc22ef7f3a703b15389616a1c3af8befcc9b7c78ab57","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:10:49.059717Z","signature_b64":"UeikEPVadBbYDIXKx6Xh8A+jU2A730xYp9hQnuIq9+gGcjFzvARTG6Oe5P7IJ5PtR0lNjbOeQJwH/Dh4ADlDCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36b32aeff24f8e43a799dc22ef7f3a703b15389616a1c3af8befcc9b7c78ab57","last_reissued_at":"2026-07-05T07:10:49.059221Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:10:49.059221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2307.03044","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":"2026-07-05T07:10:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UkYeHhl2XIuiXh31VY7jelFUfc3J5+YK7sBYg+FBk/0SUnduEuODngaBZEVAt1BiP/06I0v55bOYrs0KkEvJBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T13:16:34.592621Z"},"content_sha256":"89ba6e4db7f9854464cd0f6bdebd6fd13351215de1b49bdd19e743bb67587d46","schema_version":"1.0","event_id":"sha256:89ba6e4db7f9854464cd0f6bdebd6fd13351215de1b49bdd19e743bb67587d46"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:G2ZSV37SJ6HEHJ4Z3QRO67Z2OA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotics in finite monoidal categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.RA"],"primary_cat":"math.RT","authors_text":"Abel Lacabanne, Daniel Tubbenhauer, Pedro Vaz","submitted_at":"2023-07-06T15:09:44Z","abstract_excerpt":"We give explicit formulas for the asymptotic growth rate of the number of summands in tensor powers in certain monoidal categories with finitely many indecomposable objects, and related structures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.03044","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/2307.03044/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":"2026-07-05T07:10:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nDgsyba2f8p+LsnN17UwCbGlpgt65ONkgxuOx4FErxlvu3qZeiFJSgqzMkkLVgr7yb9dGOUsQzZIBDFe0gZDBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T13:16:34.593402Z"},"content_sha256":"c02ac65883df4bf17d9dac32e86ef824a485d2e252a0b4453f420d1cd84f88b2","schema_version":"1.0","event_id":"sha256:c02ac65883df4bf17d9dac32e86ef824a485d2e252a0b4453f420d1cd84f88b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G2ZSV37SJ6HEHJ4Z3QRO67Z2OA/bundle.json","state_url":"https://pith.science/pith/G2ZSV37SJ6HEHJ4Z3QRO67Z2OA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G2ZSV37SJ6HEHJ4Z3QRO67Z2OA/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":"2026-08-21T13:16:34Z","links":{"resolver":"https://pith.science/pith/G2ZSV37SJ6HEHJ4Z3QRO67Z2OA","bundle":"https://pith.science/pith/G2ZSV37SJ6HEHJ4Z3QRO67Z2OA/bundle.json","state":"https://pith.science/pith/G2ZSV37SJ6HEHJ4Z3QRO67Z2OA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G2ZSV37SJ6HEHJ4Z3QRO67Z2OA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:G2ZSV37SJ6HEHJ4Z3QRO67Z2OA","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":"760696285bdab6877769dd14d12a62ec36aa8236d328faa8114f7e8b2ef41ee3","cross_cats_sorted":["math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2023-07-06T15:09:44Z","title_canon_sha256":"3181f6ede0c3ef7873f61d03ea300d35d542354f09a0a5c2203e97626bdba584"},"schema_version":"1.0","source":{"id":"2307.03044","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.03044","created_at":"2026-07-05T07:10:49Z"},{"alias_kind":"arxiv_version","alias_value":"2307.03044v2","created_at":"2026-07-05T07:10:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.03044","created_at":"2026-07-05T07:10:49Z"},{"alias_kind":"pith_short_12","alias_value":"G2ZSV37SJ6HE","created_at":"2026-07-05T07:10:49Z"},{"alias_kind":"pith_short_16","alias_value":"G2ZSV37SJ6HEHJ4Z","created_at":"2026-07-05T07:10:49Z"},{"alias_kind":"pith_short_8","alias_value":"G2ZSV37S","created_at":"2026-07-05T07:10:49Z"}],"graph_snapshots":[{"event_id":"sha256:c02ac65883df4bf17d9dac32e86ef824a485d2e252a0b4453f420d1cd84f88b2","target":"graph","created_at":"2026-07-05T07:10:49Z","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/2307.03044/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give explicit formulas for the asymptotic growth rate of the number of summands in tensor powers in certain monoidal categories with finitely many indecomposable objects, and related structures.","authors_text":"Abel Lacabanne, Daniel Tubbenhauer, Pedro Vaz","cross_cats":["math.CT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2023-07-06T15:09:44Z","title":"Asymptotics in finite monoidal categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.03044","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":"sha256:89ba6e4db7f9854464cd0f6bdebd6fd13351215de1b49bdd19e743bb67587d46","target":"record","created_at":"2026-07-05T07:10:49Z","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":"760696285bdab6877769dd14d12a62ec36aa8236d328faa8114f7e8b2ef41ee3","cross_cats_sorted":["math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2023-07-06T15:09:44Z","title_canon_sha256":"3181f6ede0c3ef7873f61d03ea300d35d542354f09a0a5c2203e97626bdba584"},"schema_version":"1.0","source":{"id":"2307.03044","kind":"arxiv","version":2}},"canonical_sha256":"36b32aeff24f8e43a799dc22ef7f3a703b15389616a1c3af8befcc9b7c78ab57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36b32aeff24f8e43a799dc22ef7f3a703b15389616a1c3af8befcc9b7c78ab57","first_computed_at":"2026-07-05T07:10:49.059221Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:10:49.059221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UeikEPVadBbYDIXKx6Xh8A+jU2A730xYp9hQnuIq9+gGcjFzvARTG6Oe5P7IJ5PtR0lNjbOeQJwH/Dh4ADlDCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:10:49.059717Z","signed_message":"canonical_sha256_bytes"},"source_id":"2307.03044","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89ba6e4db7f9854464cd0f6bdebd6fd13351215de1b49bdd19e743bb67587d46","sha256:c02ac65883df4bf17d9dac32e86ef824a485d2e252a0b4453f420d1cd84f88b2"],"state_sha256":"8641f5affcb516a277175385569b187bdd742e0cc5dd3bf783e3974b896d582e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wAPTwyL52y4HzoYBY8chYUdbPilxUcYYm6lU9VlTYMjih+aip3GiEpQQtV+dMSipJ7nnEaAkAlUqrpAqgyjjAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T13:16:34.599320Z","bundle_sha256":"e8f6aff704bf022c95de3506712810395f0bc6c23641dc932c9cd2cc097be621"}}