{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:2KWMI2RD7X54BP3IKPIRMGK4WH","short_pith_number":"pith:2KWMI2RD","canonical_record":{"source":{"id":"1411.5425","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-20T02:39:55Z","cross_cats_sorted":[],"title_canon_sha256":"70fabe8897e31511ae1757d5ac18601c0ff517411325db255c1aac5b36f10c3a","abstract_canon_sha256":"804f72f42eb3b8684c5be43d5ed9a6313e33aa694ed8e6360df83685d9f2b852"},"schema_version":"1.0"},"canonical_sha256":"d2acc46a23fdfbc0bf6853d116195cb1d4d464f0ebe5296ab42502b047d54b9c","source":{"kind":"arxiv","id":"1411.5425","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.5425","created_at":"2026-05-18T00:40:42Z"},{"alias_kind":"arxiv_version","alias_value":"1411.5425v3","created_at":"2026-05-18T00:40:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.5425","created_at":"2026-05-18T00:40:42Z"},{"alias_kind":"pith_short_12","alias_value":"2KWMI2RD7X54","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2KWMI2RD7X54BP3I","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2KWMI2RD","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:2KWMI2RD7X54BP3IKPIRMGK4WH","target":"record","payload":{"canonical_record":{"source":{"id":"1411.5425","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-20T02:39:55Z","cross_cats_sorted":[],"title_canon_sha256":"70fabe8897e31511ae1757d5ac18601c0ff517411325db255c1aac5b36f10c3a","abstract_canon_sha256":"804f72f42eb3b8684c5be43d5ed9a6313e33aa694ed8e6360df83685d9f2b852"},"schema_version":"1.0"},"canonical_sha256":"d2acc46a23fdfbc0bf6853d116195cb1d4d464f0ebe5296ab42502b047d54b9c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:42.015548Z","signature_b64":"HVLr95519BR/hBMdAgpM/X37zcuvTF+AM+Cp7d8x2ZEEmfvj4hHSE5NR4yTt8mSgJL3Hfyk/xuWUiL4Dec/IAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2acc46a23fdfbc0bf6853d116195cb1d4d464f0ebe5296ab42502b047d54b9c","last_reissued_at":"2026-05-18T00:40:42.014918Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:42.014918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.5425","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:40:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WmJkAgArTySH05Lrw8g+ijjvZBGVbRZOmehV/UQQHzvVG+bi+r1ZiX1HVgP2NdwAqMN5K2JIfvrIVKIhZ7nDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:01:30.750804Z"},"content_sha256":"d4531640adce4b52b5046b9f291eea5257299b749a7a9ffe2653681892b503d6","schema_version":"1.0","event_id":"sha256:d4531640adce4b52b5046b9f291eea5257299b749a7a9ffe2653681892b503d6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:2KWMI2RD7X54BP3IKPIRMGK4WH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tangent spaces and tangent bundles for diffeological spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Enxin Wu, J. Daniel Christensen","submitted_at":"2014-11-20T02:39:55Z","abstract_excerpt":"We study how the notion of tangent space can be extended from smooth manifolds to diffeological spaces, which are generalizations of smooth manifolds that include singular spaces and infinite-dimensional spaces. We focus on two definitions. The internal tangent space of a diffeological space is defined using smooth curves into the space, and the external tangent space is defined using smooth derivations on germs of smooth functions. We prove fundamental results about these tangent spaces, compute them in many examples, and observe that while they agree for smooth manifolds and many of the exam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5425","kind":"arxiv","version":3},"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":"2026-05-18T00:40:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bh9u6nN1ScAUlVCilL6LbQJWh7Atebujm4NrhHrYjRJRJsSFKjmPG4x6tNnEN7bF7nCdQpLVxsTB8h8FrlafAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:01:30.751452Z"},"content_sha256":"a7ec90711b44b50d73d286ceae095f5ac8ba55e792b2d7ff9e6b153cb12745d1","schema_version":"1.0","event_id":"sha256:a7ec90711b44b50d73d286ceae095f5ac8ba55e792b2d7ff9e6b153cb12745d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2KWMI2RD7X54BP3IKPIRMGK4WH/bundle.json","state_url":"https://pith.science/pith/2KWMI2RD7X54BP3IKPIRMGK4WH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2KWMI2RD7X54BP3IKPIRMGK4WH/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":"2026-05-28T22:01:30Z","links":{"resolver":"https://pith.science/pith/2KWMI2RD7X54BP3IKPIRMGK4WH","bundle":"https://pith.science/pith/2KWMI2RD7X54BP3IKPIRMGK4WH/bundle.json","state":"https://pith.science/pith/2KWMI2RD7X54BP3IKPIRMGK4WH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2KWMI2RD7X54BP3IKPIRMGK4WH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2KWMI2RD7X54BP3IKPIRMGK4WH","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":"804f72f42eb3b8684c5be43d5ed9a6313e33aa694ed8e6360df83685d9f2b852","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-20T02:39:55Z","title_canon_sha256":"70fabe8897e31511ae1757d5ac18601c0ff517411325db255c1aac5b36f10c3a"},"schema_version":"1.0","source":{"id":"1411.5425","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.5425","created_at":"2026-05-18T00:40:42Z"},{"alias_kind":"arxiv_version","alias_value":"1411.5425v3","created_at":"2026-05-18T00:40:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.5425","created_at":"2026-05-18T00:40:42Z"},{"alias_kind":"pith_short_12","alias_value":"2KWMI2RD7X54","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2KWMI2RD7X54BP3I","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2KWMI2RD","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:a7ec90711b44b50d73d286ceae095f5ac8ba55e792b2d7ff9e6b153cb12745d1","target":"graph","created_at":"2026-05-18T00:40:42Z","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 study how the notion of tangent space can be extended from smooth manifolds to diffeological spaces, which are generalizations of smooth manifolds that include singular spaces and infinite-dimensional spaces. We focus on two definitions. The internal tangent space of a diffeological space is defined using smooth curves into the space, and the external tangent space is defined using smooth derivations on germs of smooth functions. We prove fundamental results about these tangent spaces, compute them in many examples, and observe that while they agree for smooth manifolds and many of the exam","authors_text":"Enxin Wu, J. Daniel Christensen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-20T02:39:55Z","title":"Tangent spaces and tangent bundles for diffeological spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5425","kind":"arxiv","version":3},"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:d4531640adce4b52b5046b9f291eea5257299b749a7a9ffe2653681892b503d6","target":"record","created_at":"2026-05-18T00:40:42Z","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":"804f72f42eb3b8684c5be43d5ed9a6313e33aa694ed8e6360df83685d9f2b852","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-20T02:39:55Z","title_canon_sha256":"70fabe8897e31511ae1757d5ac18601c0ff517411325db255c1aac5b36f10c3a"},"schema_version":"1.0","source":{"id":"1411.5425","kind":"arxiv","version":3}},"canonical_sha256":"d2acc46a23fdfbc0bf6853d116195cb1d4d464f0ebe5296ab42502b047d54b9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2acc46a23fdfbc0bf6853d116195cb1d4d464f0ebe5296ab42502b047d54b9c","first_computed_at":"2026-05-18T00:40:42.014918Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:42.014918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HVLr95519BR/hBMdAgpM/X37zcuvTF+AM+Cp7d8x2ZEEmfvj4hHSE5NR4yTt8mSgJL3Hfyk/xuWUiL4Dec/IAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:42.015548Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.5425","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4531640adce4b52b5046b9f291eea5257299b749a7a9ffe2653681892b503d6","sha256:a7ec90711b44b50d73d286ceae095f5ac8ba55e792b2d7ff9e6b153cb12745d1"],"state_sha256":"6f1b9fbc55268e89ebb8e4d335b1680fda765edff107735d152ab157c155ee29"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ydCZq/Us9fExRhALSV/VvQASeQLlgqP2fmii7b6RPa7b12dsLL9MfqwzMQB7fZUxvLeUDG100DFrdHJYEFVoDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:01:30.755142Z","bundle_sha256":"ed573ed5dffeec458f340807154dc9961ef825df454621f4aea20d28aa11a156"}}