{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:OHBYHMJQP5QSUGYFJB7QQM3AY5","short_pith_number":"pith:OHBYHMJQ","canonical_record":{"source":{"id":"2311.06099","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-11-10T15:06:05Z","cross_cats_sorted":["math.AP","math.FA"],"title_canon_sha256":"a257b3143c09f976592daa231aa235c38afbb7dad736f2c8f5ba015f569af456","abstract_canon_sha256":"67d7d72e42fc107eed08c66a491769fbe0253a9ddc4c6ec5fab2c720c3e3ad30"},"schema_version":"1.0"},"canonical_sha256":"71c383b1307f612a1b05487f083360c76c8ed510807ba496ae28a4d56dccb3b5","source":{"kind":"arxiv","id":"2311.06099","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.06099","created_at":"2026-07-05T07:11:28Z"},{"alias_kind":"arxiv_version","alias_value":"2311.06099v1","created_at":"2026-07-05T07:11:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.06099","created_at":"2026-07-05T07:11:28Z"},{"alias_kind":"pith_short_12","alias_value":"OHBYHMJQP5QS","created_at":"2026-07-05T07:11:28Z"},{"alias_kind":"pith_short_16","alias_value":"OHBYHMJQP5QSUGYF","created_at":"2026-07-05T07:11:28Z"},{"alias_kind":"pith_short_8","alias_value":"OHBYHMJQ","created_at":"2026-07-05T07:11:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:OHBYHMJQP5QSUGYFJB7QQM3AY5","target":"record","payload":{"canonical_record":{"source":{"id":"2311.06099","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-11-10T15:06:05Z","cross_cats_sorted":["math.AP","math.FA"],"title_canon_sha256":"a257b3143c09f976592daa231aa235c38afbb7dad736f2c8f5ba015f569af456","abstract_canon_sha256":"67d7d72e42fc107eed08c66a491769fbe0253a9ddc4c6ec5fab2c720c3e3ad30"},"schema_version":"1.0"},"canonical_sha256":"71c383b1307f612a1b05487f083360c76c8ed510807ba496ae28a4d56dccb3b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:11:28.073216Z","signature_b64":"KMtFFKTjFK/9OGAdJvH/ueHRgmunxG36MtW/xJaDLA1Qtj2BjoMzaFyoUBO6J8/+lmNukcrKjM8TUXPyrK7nAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71c383b1307f612a1b05487f083360c76c8ed510807ba496ae28a4d56dccb3b5","last_reissued_at":"2026-07-05T07:11:28.072830Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:11:28.072830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.06099","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:11:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Yc9RZM+ktXkg40V8PV4oZQDc0CWY4Mka60GOQjYhTDD14C68l+qC4amR4VJ806UFDxx7QTsc0fNQKrPlpv7CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T05:39:29.180444Z"},"content_sha256":"5e69e5fb7f395ae800586990dbfe7619303ff12865fc1e5c789924ddf4cdc73a","schema_version":"1.0","event_id":"sha256:5e69e5fb7f395ae800586990dbfe7619303ff12865fc1e5c789924ddf4cdc73a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:OHBYHMJQP5QSUGYFJB7QQM3AY5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the structure of flat chains with finite mass","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.CA","authors_text":"Andrea Marchese, Giovanni Alberti","submitted_at":"2023-11-10T15:06:05Z","abstract_excerpt":"We prove that every flat chain with finite mass in $\\mathbb{R}^d$ with coefficients in a normed abelian group $G$ is the restriction of a normal $G$-current to a Borel set. We deduce a characterization of real flat chains with finite mass in terms of a pointwise relation between the associated measure and vector field. We also deduce that any codimension-one real flat chain with finite mass can be written as an integral of multiplicity-one rectifiable currents, without loss of mass.\n  Given a Lipschitz homomorphism $\\phi:\\tilde G\\to G$ between two groups, we then study the associated map $\\pi$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.06099","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.06099/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:11:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uX35tENi8RX1aX9r/GE8qB6royZkRUF1LQaae3S0WXxYzn1Uo7FzIIJD6Y91Au7BWFsB/0fqDdpdjeQa+nFzCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T05:39:29.180855Z"},"content_sha256":"6b4d701c45e01ad82681c1bfce9d1dbdae7c450c4a213e79dcb95b41d0889379","schema_version":"1.0","event_id":"sha256:6b4d701c45e01ad82681c1bfce9d1dbdae7c450c4a213e79dcb95b41d0889379"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OHBYHMJQP5QSUGYFJB7QQM3AY5/bundle.json","state_url":"https://pith.science/pith/OHBYHMJQP5QSUGYFJB7QQM3AY5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OHBYHMJQP5QSUGYFJB7QQM3AY5/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":"2026-08-13T05:39:29Z","links":{"resolver":"https://pith.science/pith/OHBYHMJQP5QSUGYFJB7QQM3AY5","bundle":"https://pith.science/pith/OHBYHMJQP5QSUGYFJB7QQM3AY5/bundle.json","state":"https://pith.science/pith/OHBYHMJQP5QSUGYFJB7QQM3AY5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OHBYHMJQP5QSUGYFJB7QQM3AY5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:OHBYHMJQP5QSUGYFJB7QQM3AY5","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":"67d7d72e42fc107eed08c66a491769fbe0253a9ddc4c6ec5fab2c720c3e3ad30","cross_cats_sorted":["math.AP","math.FA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-11-10T15:06:05Z","title_canon_sha256":"a257b3143c09f976592daa231aa235c38afbb7dad736f2c8f5ba015f569af456"},"schema_version":"1.0","source":{"id":"2311.06099","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.06099","created_at":"2026-07-05T07:11:28Z"},{"alias_kind":"arxiv_version","alias_value":"2311.06099v1","created_at":"2026-07-05T07:11:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.06099","created_at":"2026-07-05T07:11:28Z"},{"alias_kind":"pith_short_12","alias_value":"OHBYHMJQP5QS","created_at":"2026-07-05T07:11:28Z"},{"alias_kind":"pith_short_16","alias_value":"OHBYHMJQP5QSUGYF","created_at":"2026-07-05T07:11:28Z"},{"alias_kind":"pith_short_8","alias_value":"OHBYHMJQ","created_at":"2026-07-05T07:11:28Z"}],"graph_snapshots":[{"event_id":"sha256:6b4d701c45e01ad82681c1bfce9d1dbdae7c450c4a213e79dcb95b41d0889379","target":"graph","created_at":"2026-07-05T07:11:28Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2311.06099/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that every flat chain with finite mass in $\\mathbb{R}^d$ with coefficients in a normed abelian group $G$ is the restriction of a normal $G$-current to a Borel set. We deduce a characterization of real flat chains with finite mass in terms of a pointwise relation between the associated measure and vector field. We also deduce that any codimension-one real flat chain with finite mass can be written as an integral of multiplicity-one rectifiable currents, without loss of mass.\n  Given a Lipschitz homomorphism $\\phi:\\tilde G\\to G$ between two groups, we then study the associated map $\\pi$","authors_text":"Andrea Marchese, Giovanni Alberti","cross_cats":["math.AP","math.FA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-11-10T15:06:05Z","title":"On the structure of flat chains with finite mass"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.06099","kind":"arxiv","version":1},"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":"sha256:5e69e5fb7f395ae800586990dbfe7619303ff12865fc1e5c789924ddf4cdc73a","target":"record","created_at":"2026-07-05T07:11:28Z","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":"67d7d72e42fc107eed08c66a491769fbe0253a9ddc4c6ec5fab2c720c3e3ad30","cross_cats_sorted":["math.AP","math.FA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-11-10T15:06:05Z","title_canon_sha256":"a257b3143c09f976592daa231aa235c38afbb7dad736f2c8f5ba015f569af456"},"schema_version":"1.0","source":{"id":"2311.06099","kind":"arxiv","version":1}},"canonical_sha256":"71c383b1307f612a1b05487f083360c76c8ed510807ba496ae28a4d56dccb3b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71c383b1307f612a1b05487f083360c76c8ed510807ba496ae28a4d56dccb3b5","first_computed_at":"2026-07-05T07:11:28.072830Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:11:28.072830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KMtFFKTjFK/9OGAdJvH/ueHRgmunxG36MtW/xJaDLA1Qtj2BjoMzaFyoUBO6J8/+lmNukcrKjM8TUXPyrK7nAA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:11:28.073216Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.06099","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e69e5fb7f395ae800586990dbfe7619303ff12865fc1e5c789924ddf4cdc73a","sha256:6b4d701c45e01ad82681c1bfce9d1dbdae7c450c4a213e79dcb95b41d0889379"],"state_sha256":"d5869a5edf503cadfa002fcd8d82c7eac3032575e22cfe7eb62bcc61210add2d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2tjtqqzX17OKwMasgjBz8wiZ0q2h3lq+iRg4WGmzFGEc82D9NQxSfpeWUYafK6hr0igyGZYQKvqmugBdUpHDDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T05:39:29.183782Z","bundle_sha256":"7bef67b8af38c44051faf50b60c504606c72c20f139a73ddbfeefd78d9e7a6c6"}}