{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:L77B22HSE47CG3GPTCOBDMXUI3","short_pith_number":"pith:L77B22HS","canonical_record":{"source":{"id":"1311.6394","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-11-25T18:33:10Z","cross_cats_sorted":[],"title_canon_sha256":"10c4b6079fab0b97d7771aec30cfafc594b97d8e864088fd897bb16ee1e3bf8f","abstract_canon_sha256":"f5bc120786a5650cd5905d8fd8332f128f0979da2177969ee1640e8dc958f574"},"schema_version":"1.0"},"canonical_sha256":"5ffe1d68f2273e236ccf989c11b2f446e191bf895b69265c847ed67c9739a017","source":{"kind":"arxiv","id":"1311.6394","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6394","created_at":"2026-05-18T02:14:18Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6394v4","created_at":"2026-05-18T02:14:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6394","created_at":"2026-05-18T02:14:18Z"},{"alias_kind":"pith_short_12","alias_value":"L77B22HSE47C","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"L77B22HSE47CG3GP","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"L77B22HS","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:L77B22HSE47CG3GPTCOBDMXUI3","target":"record","payload":{"canonical_record":{"source":{"id":"1311.6394","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-11-25T18:33:10Z","cross_cats_sorted":[],"title_canon_sha256":"10c4b6079fab0b97d7771aec30cfafc594b97d8e864088fd897bb16ee1e3bf8f","abstract_canon_sha256":"f5bc120786a5650cd5905d8fd8332f128f0979da2177969ee1640e8dc958f574"},"schema_version":"1.0"},"canonical_sha256":"5ffe1d68f2273e236ccf989c11b2f446e191bf895b69265c847ed67c9739a017","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:14:18.209768Z","signature_b64":"J4VGB2QGE8/HFxAHTOfwAC9LBIcnUbuiYJjXPSKJRFttHdDZval7yThuU3+mOZN9pCbb27G/F+DhMIntZczQBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ffe1d68f2273e236ccf989c11b2f446e191bf895b69265c847ed67c9739a017","last_reissued_at":"2026-05-18T02:14:18.209075Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:14:18.209075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.6394","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":"2026-05-18T02:14:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"skgSS1yDmWcnpuw3vICzyBMwyM7kY6SSQ01zm1gjmVeXQpvq5+9G5nfVO4Uv9EjeQ4orZRzRDw9UlN4u2JirAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T16:37:00.364489Z"},"content_sha256":"1431a947cc6fa3cc169fdf421ce2bf9974ba18d9200e88eee581b7a490cf4616","schema_version":"1.0","event_id":"sha256:1431a947cc6fa3cc169fdf421ce2bf9974ba18d9200e88eee581b7a490cf4616"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:L77B22HSE47CG3GPTCOBDMXUI3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The homotopy theory of diffeological spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Enxin Wu, J. Daniel Christensen","submitted_at":"2013-11-25T18:33:10Z","abstract_excerpt":"Diffeological spaces are generalizations of smooth manifolds. In this paper, we study the homotopy theory of diffeological spaces. We begin by proving basic properties of the smooth homotopy groups that we will need later. Then we introduce the smooth singular simplicial set $S^D(X)$ associated to a diffeological space $X$, and show that when $S^D(X)$ is fibrant, it captures smooth homotopical properties of $X$. Motivated by this, we define $X$ to be fibrant when $S^D(X)$ is, and more generally define cofibrations, fibrations and weak equivalences in the category of diffeological spaces using "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6394","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":"2026-05-18T02:14:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"retLOVUBrcvf/0OMCwYwWo+aay0SY/QVyNqHaB/zzqqagSuimg3jA+ewdn3q+7bG5ftopL7GLMs8UAN/KDs/DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T16:37:00.365201Z"},"content_sha256":"f2b4ddaadcceabe123de48e5fa76e365a3ed6c5754257d81da541dc0defa6d9c","schema_version":"1.0","event_id":"sha256:f2b4ddaadcceabe123de48e5fa76e365a3ed6c5754257d81da541dc0defa6d9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L77B22HSE47CG3GPTCOBDMXUI3/bundle.json","state_url":"https://pith.science/pith/L77B22HSE47CG3GPTCOBDMXUI3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L77B22HSE47CG3GPTCOBDMXUI3/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":"2026-06-08T16:37:00Z","links":{"resolver":"https://pith.science/pith/L77B22HSE47CG3GPTCOBDMXUI3","bundle":"https://pith.science/pith/L77B22HSE47CG3GPTCOBDMXUI3/bundle.json","state":"https://pith.science/pith/L77B22HSE47CG3GPTCOBDMXUI3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L77B22HSE47CG3GPTCOBDMXUI3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:L77B22HSE47CG3GPTCOBDMXUI3","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":"f5bc120786a5650cd5905d8fd8332f128f0979da2177969ee1640e8dc958f574","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-11-25T18:33:10Z","title_canon_sha256":"10c4b6079fab0b97d7771aec30cfafc594b97d8e864088fd897bb16ee1e3bf8f"},"schema_version":"1.0","source":{"id":"1311.6394","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6394","created_at":"2026-05-18T02:14:18Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6394v4","created_at":"2026-05-18T02:14:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6394","created_at":"2026-05-18T02:14:18Z"},{"alias_kind":"pith_short_12","alias_value":"L77B22HSE47C","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"L77B22HSE47CG3GP","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"L77B22HS","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:f2b4ddaadcceabe123de48e5fa76e365a3ed6c5754257d81da541dc0defa6d9c","target":"graph","created_at":"2026-05-18T02:14:18Z","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":"Diffeological spaces are generalizations of smooth manifolds. In this paper, we study the homotopy theory of diffeological spaces. We begin by proving basic properties of the smooth homotopy groups that we will need later. Then we introduce the smooth singular simplicial set $S^D(X)$ associated to a diffeological space $X$, and show that when $S^D(X)$ is fibrant, it captures smooth homotopical properties of $X$. Motivated by this, we define $X$ to be fibrant when $S^D(X)$ is, and more generally define cofibrations, fibrations and weak equivalences in the category of diffeological spaces using ","authors_text":"Enxin Wu, J. Daniel Christensen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-11-25T18:33:10Z","title":"The homotopy theory of diffeological spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6394","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":"sha256:1431a947cc6fa3cc169fdf421ce2bf9974ba18d9200e88eee581b7a490cf4616","target":"record","created_at":"2026-05-18T02:14:18Z","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":"f5bc120786a5650cd5905d8fd8332f128f0979da2177969ee1640e8dc958f574","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-11-25T18:33:10Z","title_canon_sha256":"10c4b6079fab0b97d7771aec30cfafc594b97d8e864088fd897bb16ee1e3bf8f"},"schema_version":"1.0","source":{"id":"1311.6394","kind":"arxiv","version":4}},"canonical_sha256":"5ffe1d68f2273e236ccf989c11b2f446e191bf895b69265c847ed67c9739a017","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ffe1d68f2273e236ccf989c11b2f446e191bf895b69265c847ed67c9739a017","first_computed_at":"2026-05-18T02:14:18.209075Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:18.209075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J4VGB2QGE8/HFxAHTOfwAC9LBIcnUbuiYJjXPSKJRFttHdDZval7yThuU3+mOZN9pCbb27G/F+DhMIntZczQBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:18.209768Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.6394","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1431a947cc6fa3cc169fdf421ce2bf9974ba18d9200e88eee581b7a490cf4616","sha256:f2b4ddaadcceabe123de48e5fa76e365a3ed6c5754257d81da541dc0defa6d9c"],"state_sha256":"b3aca3aa1819c44cb2a2f56ba130f79942897e46caf76209ccc6f899cc02510f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RjtVjBsY2HBLzTSX64N6oDe39Qu5Qxi4pdSfdZtOhZgoFiw1nux37sPwwJtquEW4iP7SoQtLEM9RLikRwd6nBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T16:37:00.369211Z","bundle_sha256":"3193e8c7636b0c88ea3f307e24234830a230e71f8aaab3abca974281ff6fbbcd"}}