{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:IWPF734ECFVFKMU5SILEQPSYII","short_pith_number":"pith:IWPF734E","canonical_record":{"source":{"id":"1304.0152","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-03-31T03:53:36Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"02ea7d6d94c727d6f53285d5eee306eeb5a6b673a192280404b86b88d50d0c63","abstract_canon_sha256":"fe12f1e758c9646f5efe14787b07637d4754facf99fbd77ea490d5e7282a61a9"},"schema_version":"1.0"},"canonical_sha256":"459e5fef84116a55329d9216483e58421a0695d39fbf19b0da801fa707c7443c","source":{"kind":"arxiv","id":"1304.0152","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0152","created_at":"2026-05-18T01:29:38Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0152v2","created_at":"2026-05-18T01:29:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0152","created_at":"2026-05-18T01:29:38Z"},{"alias_kind":"pith_short_12","alias_value":"IWPF734ECFVF","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"IWPF734ECFVFKMU5","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"IWPF734E","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:IWPF734ECFVFKMU5SILEQPSYII","target":"record","payload":{"canonical_record":{"source":{"id":"1304.0152","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-03-31T03:53:36Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"02ea7d6d94c727d6f53285d5eee306eeb5a6b673a192280404b86b88d50d0c63","abstract_canon_sha256":"fe12f1e758c9646f5efe14787b07637d4754facf99fbd77ea490d5e7282a61a9"},"schema_version":"1.0"},"canonical_sha256":"459e5fef84116a55329d9216483e58421a0695d39fbf19b0da801fa707c7443c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:38.651489Z","signature_b64":"y6chO91EYZyQ1nH8F2eEBe2FhNi+uW09I62ZETAy81umxowsu8ZrH4vKWd4DkmyafCIvOxAK76/1WoTFZFSGAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"459e5fef84116a55329d9216483e58421a0695d39fbf19b0da801fa707c7443c","last_reissued_at":"2026-05-18T01:29:38.650916Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:38.650916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.0152","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:29:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+okqpGG3foB6gUuchzba+kG8XBFe0UIIKxNy2CirL+mIpRGoRWaZjzHQmegy6P7Ph6rBVDxtPm8PbLGB9q8jAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:54:01.376086Z"},"content_sha256":"d73e807226f7781cbbf53fcffa169b1377d713d403ded48b3624a63e8d965fed","schema_version":"1.0","event_id":"sha256:d73e807226f7781cbbf53fcffa169b1377d713d403ded48b3624a63e8d965fed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:IWPF734ECFVFKMU5SILEQPSYII","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The coincidence of the homologies of integral currents and of integral singular chains, via cosheaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.AT","authors_text":"Ayato Mitsuishi","submitted_at":"2013-03-31T03:53:36Z","abstract_excerpt":"We consider the notion of metric spaces being locally Lipschitz contractible introduced by Yamaguchi, and a category of metric spaces satisfying this condition. Many objects in metric geometry including CAT-spaces and Alexandrov spaces, belong to this category. We consider the homology of integral currents with compact support in a metric space, introduced by Ambrosio and Kirchheim, and prove that it and the usual integral singular homology are isomorphic on the category. The proof of it is based on the theory of cosheaves. A method to compare the homologies associated to cosheaves is also pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0152","kind":"arxiv","version":2},"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":"2026-05-18T01:29:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dczaA5mAn7MrDBZZia/JWJ6IubRinQzRyFjwPptedyaDHJRsTxG+FECKwH9CQBKb8jp7v3hF4bPOkzoBb76cAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:54:01.376450Z"},"content_sha256":"fc447f5613e45ea25b1e7dcbad0272cef8b60049f183d3285ed4cb5eccc75502","schema_version":"1.0","event_id":"sha256:fc447f5613e45ea25b1e7dcbad0272cef8b60049f183d3285ed4cb5eccc75502"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IWPF734ECFVFKMU5SILEQPSYII/bundle.json","state_url":"https://pith.science/pith/IWPF734ECFVFKMU5SILEQPSYII/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IWPF734ECFVFKMU5SILEQPSYII/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":"2026-06-23T03:54:01Z","links":{"resolver":"https://pith.science/pith/IWPF734ECFVFKMU5SILEQPSYII","bundle":"https://pith.science/pith/IWPF734ECFVFKMU5SILEQPSYII/bundle.json","state":"https://pith.science/pith/IWPF734ECFVFKMU5SILEQPSYII/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IWPF734ECFVFKMU5SILEQPSYII/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IWPF734ECFVFKMU5SILEQPSYII","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":"fe12f1e758c9646f5efe14787b07637d4754facf99fbd77ea490d5e7282a61a9","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-03-31T03:53:36Z","title_canon_sha256":"02ea7d6d94c727d6f53285d5eee306eeb5a6b673a192280404b86b88d50d0c63"},"schema_version":"1.0","source":{"id":"1304.0152","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0152","created_at":"2026-05-18T01:29:38Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0152v2","created_at":"2026-05-18T01:29:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0152","created_at":"2026-05-18T01:29:38Z"},{"alias_kind":"pith_short_12","alias_value":"IWPF734ECFVF","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"IWPF734ECFVFKMU5","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"IWPF734E","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:fc447f5613e45ea25b1e7dcbad0272cef8b60049f183d3285ed4cb5eccc75502","target":"graph","created_at":"2026-05-18T01:29:38Z","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 consider the notion of metric spaces being locally Lipschitz contractible introduced by Yamaguchi, and a category of metric spaces satisfying this condition. Many objects in metric geometry including CAT-spaces and Alexandrov spaces, belong to this category. We consider the homology of integral currents with compact support in a metric space, introduced by Ambrosio and Kirchheim, and prove that it and the usual integral singular homology are isomorphic on the category. The proof of it is based on the theory of cosheaves. A method to compare the homologies associated to cosheaves is also pro","authors_text":"Ayato Mitsuishi","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-03-31T03:53:36Z","title":"The coincidence of the homologies of integral currents and of integral singular chains, via cosheaves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0152","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:d73e807226f7781cbbf53fcffa169b1377d713d403ded48b3624a63e8d965fed","target":"record","created_at":"2026-05-18T01:29:38Z","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":"fe12f1e758c9646f5efe14787b07637d4754facf99fbd77ea490d5e7282a61a9","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-03-31T03:53:36Z","title_canon_sha256":"02ea7d6d94c727d6f53285d5eee306eeb5a6b673a192280404b86b88d50d0c63"},"schema_version":"1.0","source":{"id":"1304.0152","kind":"arxiv","version":2}},"canonical_sha256":"459e5fef84116a55329d9216483e58421a0695d39fbf19b0da801fa707c7443c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"459e5fef84116a55329d9216483e58421a0695d39fbf19b0da801fa707c7443c","first_computed_at":"2026-05-18T01:29:38.650916Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:38.650916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y6chO91EYZyQ1nH8F2eEBe2FhNi+uW09I62ZETAy81umxowsu8ZrH4vKWd4DkmyafCIvOxAK76/1WoTFZFSGAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:38.651489Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0152","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d73e807226f7781cbbf53fcffa169b1377d713d403ded48b3624a63e8d965fed","sha256:fc447f5613e45ea25b1e7dcbad0272cef8b60049f183d3285ed4cb5eccc75502"],"state_sha256":"3a978b221cfeee97de18c8f7220473ec57b9a17c5b9c92faec1a315d40a727cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iYUfO3caDzEofN92OAXBNK26k7ITJ6bS3IL2Xgoqfzm3k+DjsD158VQ9/I9jCPNv7lxjsQ/ayVi7CTibWd+iDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T03:54:01.378435Z","bundle_sha256":"5cb06e7db996308efcab98d4f0c7c93d14c035e7bb0ea4413c7baba5d7101fc0"}}