{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:2YGEU6YAX3WHNXJ6LH7FWI4N3C","short_pith_number":"pith:2YGEU6YA","canonical_record":{"source":{"id":"1308.2457","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-08-12T04:05:38Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"4823eb23c17467c7d6b9f915ac3031d38216e3053a94b4b23e1f97488b199558","abstract_canon_sha256":"9d109a2b2e422ae279cc8b85d3019cbd09fd5de77e119788f83f44cc06031ccc"},"schema_version":"1.0"},"canonical_sha256":"d60c4a7b00beec76dd3e59fe5b238dd88efa95979742e0799a56da8a511c09f8","source":{"kind":"arxiv","id":"1308.2457","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2457","created_at":"2026-05-18T02:44:08Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2457v2","created_at":"2026-05-18T02:44:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2457","created_at":"2026-05-18T02:44:08Z"},{"alias_kind":"pith_short_12","alias_value":"2YGEU6YAX3WH","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2YGEU6YAX3WHNXJ6","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2YGEU6YA","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:2YGEU6YAX3WHNXJ6LH7FWI4N3C","target":"record","payload":{"canonical_record":{"source":{"id":"1308.2457","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-08-12T04:05:38Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"4823eb23c17467c7d6b9f915ac3031d38216e3053a94b4b23e1f97488b199558","abstract_canon_sha256":"9d109a2b2e422ae279cc8b85d3019cbd09fd5de77e119788f83f44cc06031ccc"},"schema_version":"1.0"},"canonical_sha256":"d60c4a7b00beec76dd3e59fe5b238dd88efa95979742e0799a56da8a511c09f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:08.507043Z","signature_b64":"BtTgWog+PNSXP7GKHHqrvo5qHsgW1wf6sC9JLKzxPh+pWt7lZJv/9ty8CYqlwkW1ExGM5twn5dPtnHNmrTZKCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d60c4a7b00beec76dd3e59fe5b238dd88efa95979742e0799a56da8a511c09f8","last_reissued_at":"2026-05-18T02:44:08.506654Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:08.506654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.2457","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u1ZdmD+eclsx2O1X0ixxkpua9sPOxNd0azyHzwl4AccAr+OVlxER6epcED9giu9VOpHpWk5nMBP1NqUqkHJeDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T06:35:44.765068Z"},"content_sha256":"f35aaed3965f96bf67d5bf1492ce77988d8b3a0e87eaec2b005980382d59f9b4","schema_version":"1.0","event_id":"sha256:f35aaed3965f96bf67d5bf1492ce77988d8b3a0e87eaec2b005980382d59f9b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:2YGEU6YAX3WHNXJ6LH7FWI4N3C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonasymptotic densities for shape reconstruction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CA","authors_text":"Kevin R. Vixie, Kevin Sonnanburg, Sharif Ibrahim, Thomas J. Asaki","submitted_at":"2013-08-12T04:05:38Z","abstract_excerpt":"In this work, we study the problem of reconstructing shapes from simple nonasymptotic densities measured only along shape boundaries. The particular density we study is also known as the integral area invariant and corresponds to the area of a disk centered on the boundary that is also inside the shape. It is easy to show uniqueness when these densities are known for all radii in a neighborhood of r = 0, but much less straightforward when we assume that we only know the area invariant and its derivatives for only one r > 0. We present variations of uniqueness results for reconstruction (modulo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2457","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iiddg36ON1uAzNnPGMBUvrOrrhTJBHXd3XqRVewXF2TAQx6x+mHGGvARJh+xE2UCkf3xgscMvFmSV7v1n+NtBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T06:35:44.765541Z"},"content_sha256":"7d85a77b4587a92d3eb269f7446b7c7b8ee2fa3cde71cdf129ee781320ea1029","schema_version":"1.0","event_id":"sha256:7d85a77b4587a92d3eb269f7446b7c7b8ee2fa3cde71cdf129ee781320ea1029"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2YGEU6YAX3WHNXJ6LH7FWI4N3C/bundle.json","state_url":"https://pith.science/pith/2YGEU6YAX3WHNXJ6LH7FWI4N3C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2YGEU6YAX3WHNXJ6LH7FWI4N3C/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":"2026-06-30T06:35:44Z","links":{"resolver":"https://pith.science/pith/2YGEU6YAX3WHNXJ6LH7FWI4N3C","bundle":"https://pith.science/pith/2YGEU6YAX3WHNXJ6LH7FWI4N3C/bundle.json","state":"https://pith.science/pith/2YGEU6YAX3WHNXJ6LH7FWI4N3C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2YGEU6YAX3WHNXJ6LH7FWI4N3C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2YGEU6YAX3WHNXJ6LH7FWI4N3C","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":"9d109a2b2e422ae279cc8b85d3019cbd09fd5de77e119788f83f44cc06031ccc","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-08-12T04:05:38Z","title_canon_sha256":"4823eb23c17467c7d6b9f915ac3031d38216e3053a94b4b23e1f97488b199558"},"schema_version":"1.0","source":{"id":"1308.2457","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2457","created_at":"2026-05-18T02:44:08Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2457v2","created_at":"2026-05-18T02:44:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2457","created_at":"2026-05-18T02:44:08Z"},{"alias_kind":"pith_short_12","alias_value":"2YGEU6YAX3WH","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2YGEU6YAX3WHNXJ6","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2YGEU6YA","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:7d85a77b4587a92d3eb269f7446b7c7b8ee2fa3cde71cdf129ee781320ea1029","target":"graph","created_at":"2026-05-18T02:44:08Z","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":"In this work, we study the problem of reconstructing shapes from simple nonasymptotic densities measured only along shape boundaries. The particular density we study is also known as the integral area invariant and corresponds to the area of a disk centered on the boundary that is also inside the shape. It is easy to show uniqueness when these densities are known for all radii in a neighborhood of r = 0, but much less straightforward when we assume that we only know the area invariant and its derivatives for only one r > 0. We present variations of uniqueness results for reconstruction (modulo","authors_text":"Kevin R. Vixie, Kevin Sonnanburg, Sharif Ibrahim, Thomas J. Asaki","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-08-12T04:05:38Z","title":"Nonasymptotic densities for shape reconstruction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2457","kind":"arxiv","version":2},"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:f35aaed3965f96bf67d5bf1492ce77988d8b3a0e87eaec2b005980382d59f9b4","target":"record","created_at":"2026-05-18T02:44:08Z","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":"9d109a2b2e422ae279cc8b85d3019cbd09fd5de77e119788f83f44cc06031ccc","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-08-12T04:05:38Z","title_canon_sha256":"4823eb23c17467c7d6b9f915ac3031d38216e3053a94b4b23e1f97488b199558"},"schema_version":"1.0","source":{"id":"1308.2457","kind":"arxiv","version":2}},"canonical_sha256":"d60c4a7b00beec76dd3e59fe5b238dd88efa95979742e0799a56da8a511c09f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d60c4a7b00beec76dd3e59fe5b238dd88efa95979742e0799a56da8a511c09f8","first_computed_at":"2026-05-18T02:44:08.506654Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:08.506654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BtTgWog+PNSXP7GKHHqrvo5qHsgW1wf6sC9JLKzxPh+pWt7lZJv/9ty8CYqlwkW1ExGM5twn5dPtnHNmrTZKCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:08.507043Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.2457","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f35aaed3965f96bf67d5bf1492ce77988d8b3a0e87eaec2b005980382d59f9b4","sha256:7d85a77b4587a92d3eb269f7446b7c7b8ee2fa3cde71cdf129ee781320ea1029"],"state_sha256":"cb232c15dfd4be59d9c187029ad79f7a9671373c35a43f1c2d2089086e84a6e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"td/CEbqyOHHpDRCpqS+i/2ScJ3kHtVI23gub7mRnCLjcZFOqKBGBEmE1YxKK4I0pFXJ3Fz++hBeJq8znlEOBAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T06:35:44.767532Z","bundle_sha256":"43ded86f8ab38d3e0390fb6db430598c9c953db73cd6d13dd647990a1798712b"}}