{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:AMQ67TYJBJS5JKSLJTO3O2YFDA","short_pith_number":"pith:AMQ67TYJ","canonical_record":{"source":{"id":"1903.07964","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2019-03-19T12:36:57Z","cross_cats_sorted":["math.AT","math.CT"],"title_canon_sha256":"c34838691e78dfe8de6d4b4ccbbc3b93d493badd988852bc8f12560027193992","abstract_canon_sha256":"f5406568a45e0ff42ed1c3216160bf90a7b021dbb0cf293ff217628ea0a1e703"},"schema_version":"1.0"},"canonical_sha256":"0321efcf090a65d4aa4b4cddb76b05180850e9aa87cbd17c0e8e7339646ba958","source":{"kind":"arxiv","id":"1903.07964","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.07964","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"arxiv_version","alias_value":"1903.07964v1","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07964","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"pith_short_12","alias_value":"AMQ67TYJBJS5","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"AMQ67TYJBJS5JKSL","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"AMQ67TYJ","created_at":"2026-05-18T12:33:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:AMQ67TYJBJS5JKSLJTO3O2YFDA","target":"record","payload":{"canonical_record":{"source":{"id":"1903.07964","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2019-03-19T12:36:57Z","cross_cats_sorted":["math.AT","math.CT"],"title_canon_sha256":"c34838691e78dfe8de6d4b4ccbbc3b93d493badd988852bc8f12560027193992","abstract_canon_sha256":"f5406568a45e0ff42ed1c3216160bf90a7b021dbb0cf293ff217628ea0a1e703"},"schema_version":"1.0"},"canonical_sha256":"0321efcf090a65d4aa4b4cddb76b05180850e9aa87cbd17c0e8e7339646ba958","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:53.396910Z","signature_b64":"I0EAm6dEA0rLANIaTcLYt7vwX9EbhBYk61o+ZTBi71QGlMV2+7F8i7MgEOelacRL7EfiiZWTfdLT4dUULp9KCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0321efcf090a65d4aa4b4cddb76b05180850e9aa87cbd17c0e8e7339646ba958","last_reissued_at":"2026-05-17T23:50:53.396149Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:53.396149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.07964","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":"2026-05-17T23:50:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uXMADQFENigyvhV7VemuuFToM85BhBf4N//t1naKkbx/uzX4f9Alm7/wFPNlYnQoOGgnpwhKjnABFbee0dFhAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T00:24:41.307098Z"},"content_sha256":"d88ae85e5765c6bf74b1513a8704a0386ec1ad606a3cb6dd492cbaf5c013c34f","schema_version":"1.0","event_id":"sha256:d88ae85e5765c6bf74b1513a8704a0386ec1ad606a3cb6dd492cbaf5c013c34f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:AMQ67TYJBJS5JKSLJTO3O2YFDA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hereditary species as monoidal decomposition spaces, comodule bialgebras, and operadic categories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT","math.CT"],"primary_cat":"math.CO","authors_text":"Louis Carlier","submitted_at":"2019-03-19T12:36:57Z","abstract_excerpt":"We show that Schmitt's hereditary species induce monoidal decomposition spaces, and exhibit Schmitt's bialgebra construction as an instance of the general bialgebra construction on a monoidal decomposition space. We show furthermore that this bialgebra structure coacts on the underlying restriction-species bialgebra structure so as to form a comodule bialgebra. Finally, we show that hereditary species induce a new family of examples of operadic categories in the sense of Batanin and Markl."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07964","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":""},"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":"2026-05-17T23:50:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4tBbadg37LwKYm2K+1LJkQX4mNMwOQ5JfweazJdxMc5MaPlre8S8w+z/r96/HhSn0ONwPO/+u03FtmT+QEKeBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T00:24:41.307601Z"},"content_sha256":"effb807fc7b1370e6a398dc42b6271d7c772267285352683c1e5b79201e86c46","schema_version":"1.0","event_id":"sha256:effb807fc7b1370e6a398dc42b6271d7c772267285352683c1e5b79201e86c46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AMQ67TYJBJS5JKSLJTO3O2YFDA/bundle.json","state_url":"https://pith.science/pith/AMQ67TYJBJS5JKSLJTO3O2YFDA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AMQ67TYJBJS5JKSLJTO3O2YFDA/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":"2026-08-09T00:24:41Z","links":{"resolver":"https://pith.science/pith/AMQ67TYJBJS5JKSLJTO3O2YFDA","bundle":"https://pith.science/pith/AMQ67TYJBJS5JKSLJTO3O2YFDA/bundle.json","state":"https://pith.science/pith/AMQ67TYJBJS5JKSLJTO3O2YFDA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AMQ67TYJBJS5JKSLJTO3O2YFDA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:AMQ67TYJBJS5JKSLJTO3O2YFDA","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":"f5406568a45e0ff42ed1c3216160bf90a7b021dbb0cf293ff217628ea0a1e703","cross_cats_sorted":["math.AT","math.CT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2019-03-19T12:36:57Z","title_canon_sha256":"c34838691e78dfe8de6d4b4ccbbc3b93d493badd988852bc8f12560027193992"},"schema_version":"1.0","source":{"id":"1903.07964","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.07964","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"arxiv_version","alias_value":"1903.07964v1","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07964","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"pith_short_12","alias_value":"AMQ67TYJBJS5","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"AMQ67TYJBJS5JKSL","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"AMQ67TYJ","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:effb807fc7b1370e6a398dc42b6271d7c772267285352683c1e5b79201e86c46","target":"graph","created_at":"2026-05-17T23:50:53Z","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 show that Schmitt's hereditary species induce monoidal decomposition spaces, and exhibit Schmitt's bialgebra construction as an instance of the general bialgebra construction on a monoidal decomposition space. We show furthermore that this bialgebra structure coacts on the underlying restriction-species bialgebra structure so as to form a comodule bialgebra. Finally, we show that hereditary species induce a new family of examples of operadic categories in the sense of Batanin and Markl.","authors_text":"Louis Carlier","cross_cats":["math.AT","math.CT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2019-03-19T12:36:57Z","title":"Hereditary species as monoidal decomposition spaces, comodule bialgebras, and operadic categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07964","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:d88ae85e5765c6bf74b1513a8704a0386ec1ad606a3cb6dd492cbaf5c013c34f","target":"record","created_at":"2026-05-17T23:50:53Z","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":"f5406568a45e0ff42ed1c3216160bf90a7b021dbb0cf293ff217628ea0a1e703","cross_cats_sorted":["math.AT","math.CT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2019-03-19T12:36:57Z","title_canon_sha256":"c34838691e78dfe8de6d4b4ccbbc3b93d493badd988852bc8f12560027193992"},"schema_version":"1.0","source":{"id":"1903.07964","kind":"arxiv","version":1}},"canonical_sha256":"0321efcf090a65d4aa4b4cddb76b05180850e9aa87cbd17c0e8e7339646ba958","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0321efcf090a65d4aa4b4cddb76b05180850e9aa87cbd17c0e8e7339646ba958","first_computed_at":"2026-05-17T23:50:53.396149Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:53.396149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I0EAm6dEA0rLANIaTcLYt7vwX9EbhBYk61o+ZTBi71QGlMV2+7F8i7MgEOelacRL7EfiiZWTfdLT4dUULp9KCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:53.396910Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.07964","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d88ae85e5765c6bf74b1513a8704a0386ec1ad606a3cb6dd492cbaf5c013c34f","sha256:effb807fc7b1370e6a398dc42b6271d7c772267285352683c1e5b79201e86c46"],"state_sha256":"14a73dd8379649b13d97ceeee6f49d8d598f136269a75af244a9f32d74165c90"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mSd+uz6NNIcbAdLfQCB/q+8RZfIHfszDTqU9aTm/wYmdGcDBFprKQjy4F4KPP8gxthusqAdpYllU483ZiaNECg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T00:24:41.312371Z","bundle_sha256":"b98eb6c961049350ddc7ed42921b29fc416672e563beb43e666959064e3c583c"}}