{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:XLANG3OV3ZDHANXN4VPNAVINO7","short_pith_number":"pith:XLANG3OV","schema_version":"1.0","canonical_sha256":"bac0d36dd5de467036ede55ed0550d77f277cd64c7b0e227ae33dead947ca9d0","source":{"kind":"arxiv","id":"1504.04839","version":2},"attestation_state":"computed","paper":{"title":"Some Minimal Shape Decompositions Are Nice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.DG","authors_text":"Kevin R. Vixie","submitted_at":"2015-04-19T15:00:50Z","abstract_excerpt":"In some sense, the world is composed of shapes and words, of continuous things and discrete things. The recognition and study of continuous objects in the form of shapes occupies a significant part of the effort of unraveling many geometric questions. Shapes can be rep- resented with great generality by objects called currents. While the enormous variety and representational power of currents is useful for representing a huge variety of phenomena, it also leads to the problem that knowing something is a respectable current tells you little about how nice or regular it is. In these brief notes "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1504.04839","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-19T15:00:50Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"bd8d9835cba6660a36530c58cf808539521a266f59f53b0a0b6642f700a73b94","abstract_canon_sha256":"49b9eccaa35b402cc902daa057fadd05e7769e86cfdd18bd6ae28df549bf48bf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:27.455811Z","signature_b64":"AfKVaDRMNVWPFs1r+QZI5ZqPHjVjDLcJfIYtt+NhiyVg6/vj12kw0mkyPwdKdfVonuqgcd2ElXwLV1ijcSeIDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bac0d36dd5de467036ede55ed0550d77f277cd64c7b0e227ae33dead947ca9d0","last_reissued_at":"2026-05-18T01:36:27.455276Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:27.455276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some Minimal Shape Decompositions Are Nice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.DG","authors_text":"Kevin R. Vixie","submitted_at":"2015-04-19T15:00:50Z","abstract_excerpt":"In some sense, the world is composed of shapes and words, of continuous things and discrete things. The recognition and study of continuous objects in the form of shapes occupies a significant part of the effort of unraveling many geometric questions. Shapes can be rep- resented with great generality by objects called currents. While the enormous variety and representational power of currents is useful for representing a huge variety of phenomena, it also leads to the problem that knowing something is a respectable current tells you little about how nice or regular it is. In these brief notes "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04839","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1504.04839","created_at":"2026-05-18T01:36:27.455360+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.04839v2","created_at":"2026-05-18T01:36:27.455360+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04839","created_at":"2026-05-18T01:36:27.455360+00:00"},{"alias_kind":"pith_short_12","alias_value":"XLANG3OV3ZDH","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"XLANG3OV3ZDHANXN","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"XLANG3OV","created_at":"2026-05-18T12:29:50.041715+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XLANG3OV3ZDHANXN4VPNAVINO7","json":"https://pith.science/pith/XLANG3OV3ZDHANXN4VPNAVINO7.json","graph_json":"https://pith.science/api/pith-number/XLANG3OV3ZDHANXN4VPNAVINO7/graph.json","events_json":"https://pith.science/api/pith-number/XLANG3OV3ZDHANXN4VPNAVINO7/events.json","paper":"https://pith.science/paper/XLANG3OV"},"agent_actions":{"view_html":"https://pith.science/pith/XLANG3OV3ZDHANXN4VPNAVINO7","download_json":"https://pith.science/pith/XLANG3OV3ZDHANXN4VPNAVINO7.json","view_paper":"https://pith.science/paper/XLANG3OV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.04839&json=true","fetch_graph":"https://pith.science/api/pith-number/XLANG3OV3ZDHANXN4VPNAVINO7/graph.json","fetch_events":"https://pith.science/api/pith-number/XLANG3OV3ZDHANXN4VPNAVINO7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XLANG3OV3ZDHANXN4VPNAVINO7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XLANG3OV3ZDHANXN4VPNAVINO7/action/storage_attestation","attest_author":"https://pith.science/pith/XLANG3OV3ZDHANXN4VPNAVINO7/action/author_attestation","sign_citation":"https://pith.science/pith/XLANG3OV3ZDHANXN4VPNAVINO7/action/citation_signature","submit_replication":"https://pith.science/pith/XLANG3OV3ZDHANXN4VPNAVINO7/action/replication_record"}},"created_at":"2026-05-18T01:36:27.455360+00:00","updated_at":"2026-05-18T01:36:27.455360+00:00"}