{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:OWEW2AOXQQGWJILFJYRQXHGSPF","short_pith_number":"pith:OWEW2AOX","schema_version":"1.0","canonical_sha256":"75896d01d7840d64a1654e230b9cd2796d6ad4e7036a0446e222887fde7cddf9","source":{"kind":"arxiv","id":"1506.07252","version":1},"attestation_state":"computed","paper":{"title":"Notes on Shapes of Polyhedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Richard Evan Schwartz","submitted_at":"2015-06-24T06:21:29Z","abstract_excerpt":"These are course notes I wrote for my Fall 2013 graduate topics course on geometric structures, taught at ICERM. The notes rework many of proofs in William P. Thurston's beautiful but hard-to-understand paper, \"Shapes of Polyhedra\". A number of people, both in and out of the class, found these notes very useful and so I decided to put them on the arXiv."},"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":"1506.07252","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-06-24T06:21:29Z","cross_cats_sorted":[],"title_canon_sha256":"db571f6024efc9cbcdbf6ffe36f06314f8311ff172168913765a1469662facf4","abstract_canon_sha256":"965e5549b2f0ef651305867721824ab49c5465b55ba2a7caa018e9350570937e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:54.475483Z","signature_b64":"jtLC1UjyiYtUtaASh3dpPBS8GRIIvJRAwpoba10MXRNyiSoOVidud/H84+YGm1QlGa1RnVp8vdtZ/sc+6iUSAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75896d01d7840d64a1654e230b9cd2796d6ad4e7036a0446e222887fde7cddf9","last_reissued_at":"2026-05-18T01:39:54.475046Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:54.475046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Notes on Shapes of Polyhedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Richard Evan Schwartz","submitted_at":"2015-06-24T06:21:29Z","abstract_excerpt":"These are course notes I wrote for my Fall 2013 graduate topics course on geometric structures, taught at ICERM. The notes rework many of proofs in William P. Thurston's beautiful but hard-to-understand paper, \"Shapes of Polyhedra\". A number of people, both in and out of the class, found these notes very useful and so I decided to put them on the arXiv."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07252","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1506.07252","created_at":"2026-05-18T01:39:54.475105+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.07252v1","created_at":"2026-05-18T01:39:54.475105+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07252","created_at":"2026-05-18T01:39:54.475105+00:00"},{"alias_kind":"pith_short_12","alias_value":"OWEW2AOXQQGW","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"OWEW2AOXQQGWJILF","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"OWEW2AOX","created_at":"2026-05-18T12:29:34.919912+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/OWEW2AOXQQGWJILFJYRQXHGSPF","json":"https://pith.science/pith/OWEW2AOXQQGWJILFJYRQXHGSPF.json","graph_json":"https://pith.science/api/pith-number/OWEW2AOXQQGWJILFJYRQXHGSPF/graph.json","events_json":"https://pith.science/api/pith-number/OWEW2AOXQQGWJILFJYRQXHGSPF/events.json","paper":"https://pith.science/paper/OWEW2AOX"},"agent_actions":{"view_html":"https://pith.science/pith/OWEW2AOXQQGWJILFJYRQXHGSPF","download_json":"https://pith.science/pith/OWEW2AOXQQGWJILFJYRQXHGSPF.json","view_paper":"https://pith.science/paper/OWEW2AOX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.07252&json=true","fetch_graph":"https://pith.science/api/pith-number/OWEW2AOXQQGWJILFJYRQXHGSPF/graph.json","fetch_events":"https://pith.science/api/pith-number/OWEW2AOXQQGWJILFJYRQXHGSPF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OWEW2AOXQQGWJILFJYRQXHGSPF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OWEW2AOXQQGWJILFJYRQXHGSPF/action/storage_attestation","attest_author":"https://pith.science/pith/OWEW2AOXQQGWJILFJYRQXHGSPF/action/author_attestation","sign_citation":"https://pith.science/pith/OWEW2AOXQQGWJILFJYRQXHGSPF/action/citation_signature","submit_replication":"https://pith.science/pith/OWEW2AOXQQGWJILFJYRQXHGSPF/action/replication_record"}},"created_at":"2026-05-18T01:39:54.475105+00:00","updated_at":"2026-05-18T01:39:54.475105+00:00"}