{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:LTHSML6PZKPHPDRMVNK6SK3HF4","short_pith_number":"pith:LTHSML6P","canonical_record":{"source":{"id":"1209.1087","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-09-05T19:55:24Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"3218ad7281fb7cfb9458bb25948722af7233fe347cee74402ed82dd297b0868f","abstract_canon_sha256":"a731acd07f62c6baadd462b0d2306b4a803555277087952fc7f1dbb69ac6ac41"},"schema_version":"1.0"},"canonical_sha256":"5ccf262fcfca9e778e2cab55e92b672f0373b9e23e62bcc80a377c0527e32d79","source":{"kind":"arxiv","id":"1209.1087","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1087","created_at":"2026-05-18T00:18:32Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1087v4","created_at":"2026-05-18T00:18:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1087","created_at":"2026-05-18T00:18:32Z"},{"alias_kind":"pith_short_12","alias_value":"LTHSML6PZKPH","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LTHSML6PZKPHPDRM","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LTHSML6P","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:LTHSML6PZKPHPDRMVNK6SK3HF4","target":"record","payload":{"canonical_record":{"source":{"id":"1209.1087","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-09-05T19:55:24Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"3218ad7281fb7cfb9458bb25948722af7233fe347cee74402ed82dd297b0868f","abstract_canon_sha256":"a731acd07f62c6baadd462b0d2306b4a803555277087952fc7f1dbb69ac6ac41"},"schema_version":"1.0"},"canonical_sha256":"5ccf262fcfca9e778e2cab55e92b672f0373b9e23e62bcc80a377c0527e32d79","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:32.334287Z","signature_b64":"gispn4l8zcYGblUFUK+iZzMIicKR+ybk5CAI+qlu4C3K3HmItSyePx3Jk3f3Y2MmdQFArXWX+DhFVJeoQ+QJDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ccf262fcfca9e778e2cab55e92b672f0373b9e23e62bcc80a377c0527e32d79","last_reissued_at":"2026-05-18T00:18:32.333885Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:32.333885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.1087","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:18:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/t8GmokuhyXBEBxMg8yE5Uoe5zdYxYOmQuBswg92IXeVSxnK7YAfSFkAtpQ2o5ncaMG7ULzBB3SaBnE8VWyBAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:21:52.498004Z"},"content_sha256":"5ea0e5fb252827b3bc8082166063a53fb0de59731df181f5ff1b5012883f6561","schema_version":"1.0","event_id":"sha256:5ea0e5fb252827b3bc8082166063a53fb0de59731df181f5ff1b5012883f6561"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:LTHSML6PZKPHPDRMVNK6SK3HF4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The homotopy theory of simplicial props","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Marcy Robertson, Philip Hackney","submitted_at":"2012-09-05T19:55:24Z","abstract_excerpt":"The category of (colored) props is an enhancement of the category of colored operads, and thus of the category of small categories. In this paper, the second in a series on \"higher props,\" we show that the category of all small colored simplicial props admits a cofibrantly generated model category structure. With this model structure, the forgetful functor from props to operads is a right Quillen functor."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1087","kind":"arxiv","version":4},"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":"2026-05-18T00:18:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"juBZbhsaGX6tmEumYMNmudhuZLP277v2edfeJbSDHk93plWMy6BzyhXuCP7XT4CbKUNEMDouOtDnrntJl3aYDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:21:52.498678Z"},"content_sha256":"8378635c12a3f924d7176367fbd5efa5042b4c6a04a7912be24283940a9713ef","schema_version":"1.0","event_id":"sha256:8378635c12a3f924d7176367fbd5efa5042b4c6a04a7912be24283940a9713ef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LTHSML6PZKPHPDRMVNK6SK3HF4/bundle.json","state_url":"https://pith.science/pith/LTHSML6PZKPHPDRMVNK6SK3HF4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LTHSML6PZKPHPDRMVNK6SK3HF4/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":"2026-06-04T06:21:52Z","links":{"resolver":"https://pith.science/pith/LTHSML6PZKPHPDRMVNK6SK3HF4","bundle":"https://pith.science/pith/LTHSML6PZKPHPDRMVNK6SK3HF4/bundle.json","state":"https://pith.science/pith/LTHSML6PZKPHPDRMVNK6SK3HF4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LTHSML6PZKPHPDRMVNK6SK3HF4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LTHSML6PZKPHPDRMVNK6SK3HF4","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":"a731acd07f62c6baadd462b0d2306b4a803555277087952fc7f1dbb69ac6ac41","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-09-05T19:55:24Z","title_canon_sha256":"3218ad7281fb7cfb9458bb25948722af7233fe347cee74402ed82dd297b0868f"},"schema_version":"1.0","source":{"id":"1209.1087","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1087","created_at":"2026-05-18T00:18:32Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1087v4","created_at":"2026-05-18T00:18:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1087","created_at":"2026-05-18T00:18:32Z"},{"alias_kind":"pith_short_12","alias_value":"LTHSML6PZKPH","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LTHSML6PZKPHPDRM","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LTHSML6P","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:8378635c12a3f924d7176367fbd5efa5042b4c6a04a7912be24283940a9713ef","target":"graph","created_at":"2026-05-18T00:18:32Z","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":"The category of (colored) props is an enhancement of the category of colored operads, and thus of the category of small categories. In this paper, the second in a series on \"higher props,\" we show that the category of all small colored simplicial props admits a cofibrantly generated model category structure. With this model structure, the forgetful functor from props to operads is a right Quillen functor.","authors_text":"Marcy Robertson, Philip Hackney","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-09-05T19:55:24Z","title":"The homotopy theory of simplicial props"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1087","kind":"arxiv","version":4},"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":"sha256:5ea0e5fb252827b3bc8082166063a53fb0de59731df181f5ff1b5012883f6561","target":"record","created_at":"2026-05-18T00:18:32Z","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":"a731acd07f62c6baadd462b0d2306b4a803555277087952fc7f1dbb69ac6ac41","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-09-05T19:55:24Z","title_canon_sha256":"3218ad7281fb7cfb9458bb25948722af7233fe347cee74402ed82dd297b0868f"},"schema_version":"1.0","source":{"id":"1209.1087","kind":"arxiv","version":4}},"canonical_sha256":"5ccf262fcfca9e778e2cab55e92b672f0373b9e23e62bcc80a377c0527e32d79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ccf262fcfca9e778e2cab55e92b672f0373b9e23e62bcc80a377c0527e32d79","first_computed_at":"2026-05-18T00:18:32.333885Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:32.333885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gispn4l8zcYGblUFUK+iZzMIicKR+ybk5CAI+qlu4C3K3HmItSyePx3Jk3f3Y2MmdQFArXWX+DhFVJeoQ+QJDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:32.334287Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.1087","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ea0e5fb252827b3bc8082166063a53fb0de59731df181f5ff1b5012883f6561","sha256:8378635c12a3f924d7176367fbd5efa5042b4c6a04a7912be24283940a9713ef"],"state_sha256":"b40fcc1344fbf26b21ffa93524c20a41822395a6d2edb054e7b07702798663a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kvHXBmCqcxEJ+vFZq+ZpMuLtNdBatHs0C6ssp2P5Jp8FcATQn2ZEd0UYhskewMmS+UQRStctoQ1fdQv59B3AAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T06:21:52.502389Z","bundle_sha256":"51e3a79dfc80038ab2d2d16a8d6d3b14152f6e1ca9dc0a9470d55046b4611e94"}}