{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:HA67SXAK6IHLIXK6LKGX72M2NF","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":"141d833b57de1c0852e5fe2365c045fd10feb0a3719529b01d5132341b8a5b14","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-07-10T17:30:54Z","title_canon_sha256":"e77e9b5db49ee651a0aed900c79ca97eb21caf1c81b3ad4b8885c7c945579ceb"},"schema_version":"1.0","source":{"id":"0807.1704","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.1704","created_at":"2026-05-18T00:37:49Z"},{"alias_kind":"arxiv_version","alias_value":"0807.1704v4","created_at":"2026-05-18T00:37:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.1704","created_at":"2026-05-18T00:37:49Z"},{"alias_kind":"pith_short_12","alias_value":"HA67SXAK6IHL","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"HA67SXAK6IHLIXK6","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"HA67SXAK","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:0ec399eed227503ef464dd082059069c293eb16f2b6abec9dcdfa69d0c6866b3","target":"graph","created_at":"2026-05-18T00:37:49Z","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"},"paper":{"abstract_excerpt":"A \"Chen space\" is a set X equipped with a collection of \"plots\" - maps from convex sets to X - satisfying three simple axioms. While an individual Chen space can be much worse than a smooth manifold, the category of all Chen spaces is much better behaved than the category of smooth manifolds. For example, any subspace or quotient space of a Chen space is a Chen space, and the space of smooth maps between Chen spaces is again a Chen space. Souriau's \"diffeological spaces\" share these convenient properties. Here we give a unified treatment of both formalisms. Following ideas of Dubuc, we show th","authors_text":"Alexander E. Hoffnung, John C. Baez","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-07-10T17:30:54Z","title":"Convenient Categories of Smooth Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.1704","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:ecc27b72edf86f8e80bf0153bf22a4e9829b439de25ddea2cff5ddd0617c3baf","target":"record","created_at":"2026-05-18T00:37:49Z","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":"141d833b57de1c0852e5fe2365c045fd10feb0a3719529b01d5132341b8a5b14","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-07-10T17:30:54Z","title_canon_sha256":"e77e9b5db49ee651a0aed900c79ca97eb21caf1c81b3ad4b8885c7c945579ceb"},"schema_version":"1.0","source":{"id":"0807.1704","kind":"arxiv","version":4}},"canonical_sha256":"383df95c0af20eb45d5e5a8d7fe99a69436ea4a9da5e6a327a3e5ddcf8a19bba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"383df95c0af20eb45d5e5a8d7fe99a69436ea4a9da5e6a327a3e5ddcf8a19bba","first_computed_at":"2026-05-18T00:37:49.226985Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:49.226985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9ORNCyim4UMvs6+Ikw1uixKWCbAOFG6RfegEFsDeFYTjcgV5IVJVvP0J5lQYkqIE7EO0ka4KVMTTFCtiRqbFBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:49.227558Z","signed_message":"canonical_sha256_bytes"},"source_id":"0807.1704","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ecc27b72edf86f8e80bf0153bf22a4e9829b439de25ddea2cff5ddd0617c3baf","sha256:0ec399eed227503ef464dd082059069c293eb16f2b6abec9dcdfa69d0c6866b3"],"state_sha256":"e0f24404c186ebc82d7eeb9c8b330393f481521f78b959d0e5088748dc7956fc"}