{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZTC25X7S4CX6XG2SUAJAIJQNCR","short_pith_number":"pith:ZTC25X7S","canonical_record":{"source":{"id":"1502.00168","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-31T21:54:11Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"25efc1668572a19135f1e7759a77fb68ba21b906f855af1e69222c8fc3dd40a2","abstract_canon_sha256":"f954d0daae3b8ff152f50283c0fccbc4413736a0ebf4196613ca05e23a1f8c5f"},"schema_version":"1.0"},"canonical_sha256":"ccc5aedff2e0afeb9b52a01204260d144b5bb6aa150a2cf8979834de493f10df","source":{"kind":"arxiv","id":"1502.00168","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.00168","created_at":"2026-05-18T01:20:36Z"},{"alias_kind":"arxiv_version","alias_value":"1502.00168v1","created_at":"2026-05-18T01:20:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00168","created_at":"2026-05-18T01:20:36Z"},{"alias_kind":"pith_short_12","alias_value":"ZTC25X7S4CX6","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZTC25X7S4CX6XG2S","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZTC25X7S","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZTC25X7S4CX6XG2SUAJAIJQNCR","target":"record","payload":{"canonical_record":{"source":{"id":"1502.00168","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-31T21:54:11Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"25efc1668572a19135f1e7759a77fb68ba21b906f855af1e69222c8fc3dd40a2","abstract_canon_sha256":"f954d0daae3b8ff152f50283c0fccbc4413736a0ebf4196613ca05e23a1f8c5f"},"schema_version":"1.0"},"canonical_sha256":"ccc5aedff2e0afeb9b52a01204260d144b5bb6aa150a2cf8979834de493f10df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:36.876196Z","signature_b64":"znxpzUJnzFAq2PwKfZgvUDevvSA6m0DXoz7yWV6X4WA3kEjIPs4VwMZGn6b0rR1LLOuD/j4h5rxveVp0bKX+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccc5aedff2e0afeb9b52a01204260d144b5bb6aa150a2cf8979834de493f10df","last_reissued_at":"2026-05-18T01:20:36.875565Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:36.875565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.00168","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":"2026-05-18T01:20:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zs7pH8xJ/vU4264uouhbIYMviRI/BV1ZoiSWCIh+NjxuKgm9jxpGmJ84FjzhltV6IQQjDVym0shXrhjgI5eaCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:34:08.597010Z"},"content_sha256":"590fdff2d84e54820ff473fa765793ff0a23fc5ec832930371440c0cb6d60675","schema_version":"1.0","event_id":"sha256:590fdff2d84e54820ff473fa765793ff0a23fc5ec832930371440c0cb6d60675"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZTC25X7S4CX6XG2SUAJAIJQNCR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the role of sharp chains in the transport theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Lior Falach, Reuven Segev","submitted_at":"2015-01-31T21:54:11Z","abstract_excerpt":"A generalized transport theorem for convecting irregular domains is presented in the setting of Federer's geometric measure theory. A prototypical $r$-dimensional domain is viewed as a flat $r$-chain of finite mass in an open set of an $n$-dimensional Euclidean space. The evolution of such a generalized domain in time is assumed to be in accordance to a bi-Lipschitz type map. The induced curve is shown to be continuous with respect to the flat norm and differential with respect to the sharp norm on currents in $\\mathbb{R}^{n}$. A time dependent property is naturally assigned to the evolving re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00168","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":""},"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":"2026-05-18T01:20:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8+3JbwN3MMHqQ+F8DaNVTYa9B39KmGT4bq9AzFquAj1p3nEXikTODD/BOpkWf/PZp8M0fFPzzel/gynHUDpaBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:34:08.597705Z"},"content_sha256":"bd95660af5515eb4e465812d01a28ee5fcee91bc6cbd333144e0946b7dcf0a3f","schema_version":"1.0","event_id":"sha256:bd95660af5515eb4e465812d01a28ee5fcee91bc6cbd333144e0946b7dcf0a3f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZTC25X7S4CX6XG2SUAJAIJQNCR/bundle.json","state_url":"https://pith.science/pith/ZTC25X7S4CX6XG2SUAJAIJQNCR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZTC25X7S4CX6XG2SUAJAIJQNCR/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":"2026-06-11T08:34:08Z","links":{"resolver":"https://pith.science/pith/ZTC25X7S4CX6XG2SUAJAIJQNCR","bundle":"https://pith.science/pith/ZTC25X7S4CX6XG2SUAJAIJQNCR/bundle.json","state":"https://pith.science/pith/ZTC25X7S4CX6XG2SUAJAIJQNCR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZTC25X7S4CX6XG2SUAJAIJQNCR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZTC25X7S4CX6XG2SUAJAIJQNCR","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":"f954d0daae3b8ff152f50283c0fccbc4413736a0ebf4196613ca05e23a1f8c5f","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-31T21:54:11Z","title_canon_sha256":"25efc1668572a19135f1e7759a77fb68ba21b906f855af1e69222c8fc3dd40a2"},"schema_version":"1.0","source":{"id":"1502.00168","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.00168","created_at":"2026-05-18T01:20:36Z"},{"alias_kind":"arxiv_version","alias_value":"1502.00168v1","created_at":"2026-05-18T01:20:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00168","created_at":"2026-05-18T01:20:36Z"},{"alias_kind":"pith_short_12","alias_value":"ZTC25X7S4CX6","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZTC25X7S4CX6XG2S","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZTC25X7S","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:bd95660af5515eb4e465812d01a28ee5fcee91bc6cbd333144e0946b7dcf0a3f","target":"graph","created_at":"2026-05-18T01:20:36Z","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":"A generalized transport theorem for convecting irregular domains is presented in the setting of Federer's geometric measure theory. A prototypical $r$-dimensional domain is viewed as a flat $r$-chain of finite mass in an open set of an $n$-dimensional Euclidean space. The evolution of such a generalized domain in time is assumed to be in accordance to a bi-Lipschitz type map. The induced curve is shown to be continuous with respect to the flat norm and differential with respect to the sharp norm on currents in $\\mathbb{R}^{n}$. A time dependent property is naturally assigned to the evolving re","authors_text":"Lior Falach, Reuven Segev","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-31T21:54:11Z","title":"On the role of sharp chains in the transport theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00168","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":"sha256:590fdff2d84e54820ff473fa765793ff0a23fc5ec832930371440c0cb6d60675","target":"record","created_at":"2026-05-18T01:20:36Z","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":"f954d0daae3b8ff152f50283c0fccbc4413736a0ebf4196613ca05e23a1f8c5f","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-31T21:54:11Z","title_canon_sha256":"25efc1668572a19135f1e7759a77fb68ba21b906f855af1e69222c8fc3dd40a2"},"schema_version":"1.0","source":{"id":"1502.00168","kind":"arxiv","version":1}},"canonical_sha256":"ccc5aedff2e0afeb9b52a01204260d144b5bb6aa150a2cf8979834de493f10df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ccc5aedff2e0afeb9b52a01204260d144b5bb6aa150a2cf8979834de493f10df","first_computed_at":"2026-05-18T01:20:36.875565Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:36.875565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"znxpzUJnzFAq2PwKfZgvUDevvSA6m0DXoz7yWV6X4WA3kEjIPs4VwMZGn6b0rR1LLOuD/j4h5rxveVp0bKX+CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:36.876196Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.00168","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:590fdff2d84e54820ff473fa765793ff0a23fc5ec832930371440c0cb6d60675","sha256:bd95660af5515eb4e465812d01a28ee5fcee91bc6cbd333144e0946b7dcf0a3f"],"state_sha256":"cf20aaaa451950dccb24a9bc4374dc46a9b96780067e262db5550428ee97cc2c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"esfdsA0HoFiIn2iICEDWu+DXv0eZrxZcQDooWwSLVqOwcczq8bKmccF1M0DDCD19A1fGg9ZMQIHunpbZFQ86Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T08:34:08.601793Z","bundle_sha256":"8478ea605bf673cca3b3da88325153d7d3ee90ad071d390b43a1383e1057b044"}}