{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:O7YJQP3DP4QJ44ISIBBNFABXDR","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":"b4f3257a12c34d1d5b27ce255c734390f3dbbcd43b92cd2cbbafc44566596074","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-07-29T07:22:40Z","title_canon_sha256":"45c83bac601056a476bb322d41b2924ee34718d4363d3da6a6aacc5eec1b4c6d"},"schema_version":"1.0","source":{"id":"0907.5057","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.5057","created_at":"2026-05-18T02:12:46Z"},{"alias_kind":"arxiv_version","alias_value":"0907.5057v1","created_at":"2026-05-18T02:12:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.5057","created_at":"2026-05-18T02:12:46Z"},{"alias_kind":"pith_short_12","alias_value":"O7YJQP3DP4QJ","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"O7YJQP3DP4QJ44IS","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"O7YJQP3D","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:6271bde82e7c773a875d76d628f9e04155b2c295567ef128138f4897ea0f04d5","target":"graph","created_at":"2026-05-18T02:12:46Z","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 study the shape of inflated surfaces introduced in \\cite{B1} and \\cite{P1}. More precisely, we analyze profiles of surfaces obtained by inflating a convex polyhedron, or more generally an almost everywhere flat surface, with a symmetry plane. We show that such profiles are in a one-parameter family of curves which we describe explicitly as the solutions of a certain differential equation.","authors_text":"Igor Pak, Jean-Marc Schlenker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-07-29T07:22:40Z","title":"Profiles of inflated surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.5057","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":"sha256:937fafdf9759348c60d61ebc23c7d1601edfc727c804bb74358eedcbd5a89431","target":"record","created_at":"2026-05-18T02:12:46Z","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":"b4f3257a12c34d1d5b27ce255c734390f3dbbcd43b92cd2cbbafc44566596074","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-07-29T07:22:40Z","title_canon_sha256":"45c83bac601056a476bb322d41b2924ee34718d4363d3da6a6aacc5eec1b4c6d"},"schema_version":"1.0","source":{"id":"0907.5057","kind":"arxiv","version":1}},"canonical_sha256":"77f0983f637f209e71124042d280371c700fee63e1fc6f26d64d9d336ba49343","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77f0983f637f209e71124042d280371c700fee63e1fc6f26d64d9d336ba49343","first_computed_at":"2026-05-18T02:12:46.778220Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:12:46.778220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lUl3M4ZxXzPL6bpjBua7MpbpzIl0PAp256y6ASa06ljmrAWyI88mzfq0Jo0aVGP0247X0hQH6sbTeU0l68TODg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:12:46.778958Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.5057","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:937fafdf9759348c60d61ebc23c7d1601edfc727c804bb74358eedcbd5a89431","sha256:6271bde82e7c773a875d76d628f9e04155b2c295567ef128138f4897ea0f04d5"],"state_sha256":"4aeb4f135e35a0193e866de9589e8038f6a04de30edcb277dbf5218a00e9ad1c"}