{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:SP5JFIP7EDJDZGRHN2LLE33FIE","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":"4025477122ac5d91f1097f366c60e6e8da07b503b9f61cecdbe9937bc647aa0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2009-12-22T17:29:28Z","title_canon_sha256":"914ca2f8891fd060a150b5edc0170b55bf199fc130669b8fdc0fd1f6ce224ca9"},"schema_version":"1.0","source":{"id":"0912.4464","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.4464","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"arxiv_version","alias_value":"0912.4464v2","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.4464","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"pith_short_12","alias_value":"SP5JFIP7EDJD","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"SP5JFIP7EDJDZGRH","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"SP5JFIP7","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:cb5d662fe8831b3722a691a9738fe1efdc6d454b3244221b5d8a030b480e2924","target":"graph","created_at":"2026-05-18T04:39:59Z","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 introduce the notion of a lax monoidal fibration and we show how it can be conveniently used to deal with various algebraic structures that play an important role in some definitions of the opetopic sets (Baez-Dolan, Hermida-Makkai-Power). We present the 'standard' such structures, the exponential fibrations of basic fibrations and three areas of applications. First area is related to the T-categories of A. Burroni. The monoids in the Burroni lax monoidal fibrations form the fibration of T-categories. The construction of the relative Burroni fibrations and free T-categories in this context,","authors_text":"Marek Zawadowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2009-12-22T17:29:28Z","title":"Lax Monoidal Fibrations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.4464","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":"sha256:55ad56741544f17144574821b304f9c46b637693d62fd0728f382a7084749f31","target":"record","created_at":"2026-05-18T04:39:59Z","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":"4025477122ac5d91f1097f366c60e6e8da07b503b9f61cecdbe9937bc647aa0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2009-12-22T17:29:28Z","title_canon_sha256":"914ca2f8891fd060a150b5edc0170b55bf199fc130669b8fdc0fd1f6ce224ca9"},"schema_version":"1.0","source":{"id":"0912.4464","kind":"arxiv","version":2}},"canonical_sha256":"93fa92a1ff20d23c9a276e96b26f65412995192a6df4e0bf8a5c6eddc9db40f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93fa92a1ff20d23c9a276e96b26f65412995192a6df4e0bf8a5c6eddc9db40f8","first_computed_at":"2026-05-18T04:39:59.378408Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:59.378408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"samu36zMWhjiQn/BNtVf/5SOOiW0BZV8fRz0ibVT58bP08LBfOBKmTiGk9362pH+JWbE0xFKGaYAR0UQ8ZFZDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:59.378948Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.4464","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55ad56741544f17144574821b304f9c46b637693d62fd0728f382a7084749f31","sha256:cb5d662fe8831b3722a691a9738fe1efdc6d454b3244221b5d8a030b480e2924"],"state_sha256":"665eb230f6ab1147fda2645094ec44e697e1a030f32ba4ffd258190cb149cbcc"}