{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ARV3NMIA4CAE4DSRPVBELOFVTR","short_pith_number":"pith:ARV3NMIA","canonical_record":{"source":{"id":"1404.4796","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-04-18T14:28:11Z","cross_cats_sorted":[],"title_canon_sha256":"fe57c00a46876a1a23f4050f8bc030d31b550862d949ea4977f1066718a9aeba","abstract_canon_sha256":"62528c52f6d9277b4caa9701e566110be8bf290c2c956c94da0b5221bae41fe0"},"schema_version":"1.0"},"canonical_sha256":"046bb6b100e0804e0e517d4245b8b59c4c87a4b849d2ff1d88940b5310bce3ce","source":{"kind":"arxiv","id":"1404.4796","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4796","created_at":"2026-05-18T02:38:29Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4796v2","created_at":"2026-05-18T02:38:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4796","created_at":"2026-05-18T02:38:29Z"},{"alias_kind":"pith_short_12","alias_value":"ARV3NMIA4CAE","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"ARV3NMIA4CAE4DSR","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"ARV3NMIA","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ARV3NMIA4CAE4DSRPVBELOFVTR","target":"record","payload":{"canonical_record":{"source":{"id":"1404.4796","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-04-18T14:28:11Z","cross_cats_sorted":[],"title_canon_sha256":"fe57c00a46876a1a23f4050f8bc030d31b550862d949ea4977f1066718a9aeba","abstract_canon_sha256":"62528c52f6d9277b4caa9701e566110be8bf290c2c956c94da0b5221bae41fe0"},"schema_version":"1.0"},"canonical_sha256":"046bb6b100e0804e0e517d4245b8b59c4c87a4b849d2ff1d88940b5310bce3ce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:29.642559Z","signature_b64":"VEYngfOiKmJolDcW9yovODsx1OllEI7OKRj74UmkLUWdvUXWjZuyZoxCqdvwveUYMvEZYjx8ltKmf94WLMcUCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"046bb6b100e0804e0e517d4245b8b59c4c87a4b849d2ff1d88940b5310bce3ce","last_reissued_at":"2026-05-18T02:38:29.641944Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:29.641944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.4796","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":"2026-05-18T02:38:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ChQYLvVJvdmBQBaaMVnitvtOXKV5xyfVBU7SBs02yvJR4azIJcF+lv6Hw4UClcuDL0Hc2fJ53Iw4vC6RUmtWBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T07:53:13.496090Z"},"content_sha256":"c70125dad02c9386866e5023ab154dca34ca842c524fcb19f16565b64c091196","schema_version":"1.0","event_id":"sha256:c70125dad02c9386866e5023ab154dca34ca842c524fcb19f16565b64c091196"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ARV3NMIA4CAE4DSRPVBELOFVTR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homology Classes of Semi-Algebraic Sets and Mass Minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Quentin Funk","submitted_at":"2014-04-18T14:28:11Z","abstract_excerpt":"We associate to any compact semi-algebraic set $X \\subset \\mathbb R^n$ a chain complex of currents $S_\\ast (X)$ generated by integration along semi-algebraic submanifolds and we analyze the corresponding homology groups. In particular, we show that these homology groups satisfy the Eilenberg-Steenrod axioms and further, that they are isomorphic to both the ordinary singular homology groups of $X$ and to the homology groups generated by the integral currents supported on $X$. Using this result and a certain neighborhood of $X$, we are able to prove homological mass minimization for integral cur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4796","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":"2026-05-18T02:38:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NE56C7JATybZsL6HW1/z/pglCdeF8dl9blFdPcr4oJ9EDzvpG4KIkTcQI9fktX6w1l/gRsSsAP62+BnTc04oBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T07:53:13.496454Z"},"content_sha256":"0123e60c031b494d05522949e895fa7eacd9a399551848d8986006c160f7315e","schema_version":"1.0","event_id":"sha256:0123e60c031b494d05522949e895fa7eacd9a399551848d8986006c160f7315e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ARV3NMIA4CAE4DSRPVBELOFVTR/bundle.json","state_url":"https://pith.science/pith/ARV3NMIA4CAE4DSRPVBELOFVTR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ARV3NMIA4CAE4DSRPVBELOFVTR/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":"2026-07-02T07:53:13Z","links":{"resolver":"https://pith.science/pith/ARV3NMIA4CAE4DSRPVBELOFVTR","bundle":"https://pith.science/pith/ARV3NMIA4CAE4DSRPVBELOFVTR/bundle.json","state":"https://pith.science/pith/ARV3NMIA4CAE4DSRPVBELOFVTR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ARV3NMIA4CAE4DSRPVBELOFVTR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ARV3NMIA4CAE4DSRPVBELOFVTR","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":"62528c52f6d9277b4caa9701e566110be8bf290c2c956c94da0b5221bae41fe0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-04-18T14:28:11Z","title_canon_sha256":"fe57c00a46876a1a23f4050f8bc030d31b550862d949ea4977f1066718a9aeba"},"schema_version":"1.0","source":{"id":"1404.4796","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4796","created_at":"2026-05-18T02:38:29Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4796v2","created_at":"2026-05-18T02:38:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4796","created_at":"2026-05-18T02:38:29Z"},{"alias_kind":"pith_short_12","alias_value":"ARV3NMIA4CAE","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"ARV3NMIA4CAE4DSR","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"ARV3NMIA","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:0123e60c031b494d05522949e895fa7eacd9a399551848d8986006c160f7315e","target":"graph","created_at":"2026-05-18T02:38:29Z","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 associate to any compact semi-algebraic set $X \\subset \\mathbb R^n$ a chain complex of currents $S_\\ast (X)$ generated by integration along semi-algebraic submanifolds and we analyze the corresponding homology groups. In particular, we show that these homology groups satisfy the Eilenberg-Steenrod axioms and further, that they are isomorphic to both the ordinary singular homology groups of $X$ and to the homology groups generated by the integral currents supported on $X$. Using this result and a certain neighborhood of $X$, we are able to prove homological mass minimization for integral cur","authors_text":"Quentin Funk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-04-18T14:28:11Z","title":"Homology Classes of Semi-Algebraic Sets and Mass Minimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4796","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:c70125dad02c9386866e5023ab154dca34ca842c524fcb19f16565b64c091196","target":"record","created_at":"2026-05-18T02:38:29Z","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":"62528c52f6d9277b4caa9701e566110be8bf290c2c956c94da0b5221bae41fe0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-04-18T14:28:11Z","title_canon_sha256":"fe57c00a46876a1a23f4050f8bc030d31b550862d949ea4977f1066718a9aeba"},"schema_version":"1.0","source":{"id":"1404.4796","kind":"arxiv","version":2}},"canonical_sha256":"046bb6b100e0804e0e517d4245b8b59c4c87a4b849d2ff1d88940b5310bce3ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"046bb6b100e0804e0e517d4245b8b59c4c87a4b849d2ff1d88940b5310bce3ce","first_computed_at":"2026-05-18T02:38:29.641944Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:29.641944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VEYngfOiKmJolDcW9yovODsx1OllEI7OKRj74UmkLUWdvUXWjZuyZoxCqdvwveUYMvEZYjx8ltKmf94WLMcUCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:29.642559Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.4796","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c70125dad02c9386866e5023ab154dca34ca842c524fcb19f16565b64c091196","sha256:0123e60c031b494d05522949e895fa7eacd9a399551848d8986006c160f7315e"],"state_sha256":"bb065e3cae163e9ef43126f0bf98190844087a7381133785005e7987d7280327"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vPd9AO822tCmXb1L2zOfeJglqj4tmEih7lBwfe4mFDgdQ2Xi4lYeddFSqqe6qjHEjv098OBDYKohNKT23f1mCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T07:53:13.498389Z","bundle_sha256":"95c0c339627ee97907c01d8ad47361272640b7a4b28ebc76ce4fbc0990c021bc"}}