{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:7JOLHEF6LSAXVJ3NUWJX4UAMYC","short_pith_number":"pith:7JOLHEF6","canonical_record":{"source":{"id":"1809.07943","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-21T04:39:48Z","cross_cats_sorted":["cs.CG","cs.NA","math.FA","math.NA"],"title_canon_sha256":"b21f5bd63ca19f73946901bb8e5f8e35b4ce6e5d1223b4dd62440905ee058b73","abstract_canon_sha256":"f1ee3b7020f0ffc25939e3d155c1bb2b774ca14216e1cf5a693e3b2f7d59d088"},"schema_version":"1.0"},"canonical_sha256":"fa5cb390be5c817aa76da5937e500cc0b0ae8c60fd15819d980dec4172017b61","source":{"kind":"arxiv","id":"1809.07943","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.07943","created_at":"2026-07-05T00:00:12Z"},{"alias_kind":"arxiv_version","alias_value":"1809.07943v2","created_at":"2026-07-05T00:00:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.07943","created_at":"2026-07-05T00:00:12Z"},{"alias_kind":"pith_short_12","alias_value":"7JOLHEF6LSAX","created_at":"2026-07-05T00:00:12Z"},{"alias_kind":"pith_short_16","alias_value":"7JOLHEF6LSAXVJ3N","created_at":"2026-07-05T00:00:12Z"},{"alias_kind":"pith_short_8","alias_value":"7JOLHEF6","created_at":"2026-07-05T00:00:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:7JOLHEF6LSAXVJ3NUWJX4UAMYC","target":"record","payload":{"canonical_record":{"source":{"id":"1809.07943","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-21T04:39:48Z","cross_cats_sorted":["cs.CG","cs.NA","math.FA","math.NA"],"title_canon_sha256":"b21f5bd63ca19f73946901bb8e5f8e35b4ce6e5d1223b4dd62440905ee058b73","abstract_canon_sha256":"f1ee3b7020f0ffc25939e3d155c1bb2b774ca14216e1cf5a693e3b2f7d59d088"},"schema_version":"1.0"},"canonical_sha256":"fa5cb390be5c817aa76da5937e500cc0b0ae8c60fd15819d980dec4172017b61","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:00:12.870145Z","signature_b64":"ju6bG0mRzqvuVNGG7SI5dby1egHgU1AHSgr4PzqrrvxhfLKUnh7l1/hhOyJXSVc/MdWf9p8et6oBFnlWDceLDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa5cb390be5c817aa76da5937e500cc0b0ae8c60fd15819d980dec4172017b61","last_reissued_at":"2026-07-05T00:00:12.869669Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:00:12.869669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.07943","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":"2026-07-05T00:00:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fZfpUc3F6e4NYVESgK+vNbOUMyYmF+pxYryAgi58vu4xrFbgJpRnf+7YxTb++6273ExSHHysJVCUYfC2h41zDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T12:35:09.996375Z"},"content_sha256":"7d19eec3c8993aee9b78c6ac95eb38e935782c7cea806335e57434be31b62c70","schema_version":"1.0","event_id":"sha256:7d19eec3c8993aee9b78c6ac95eb38e935782c7cea806335e57434be31b62c70"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:7JOLHEF6LSAXVJ3NUWJX4UAMYC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Total Variation Isoperimetric Profiles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.NA","math.FA","math.NA"],"primary_cat":"math.OC","authors_text":"Daryl DeFord, Hugo Lavenant, Justin Solomon, Zachary Schutzman","submitted_at":"2018-09-21T04:39:48Z","abstract_excerpt":"Applications such as political redistricting demand quantitative measures of geometric compactness to distinguish between simple and contorted shapes. While the isoperimetric quotient, or ratio of area to perimeter squared, is commonly used in practice, it is sensitive to noisy data and irrelevant geographic features like coastline. These issues are addressed in theory by the isoperimetric profile, which plots the minimum perimeter needed to inscribe regions of different prescribed areas within the boundary of a shape. Efficient algorithms for computing this profile, however, are not known in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07943","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1809.07943/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:00:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AqSDAqp9jOjheeiVDnBELp1jpTjKojuJJcJD7LSsEVoCEDudLD1iH3SncJsS7pZavi31QcJWog6bi/u0lNhHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T12:35:09.997061Z"},"content_sha256":"04c97d768ea1c0a3b10f3fe7293f20924b9efc06ce8298578d2c6cc36e9872db","schema_version":"1.0","event_id":"sha256:04c97d768ea1c0a3b10f3fe7293f20924b9efc06ce8298578d2c6cc36e9872db"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7JOLHEF6LSAXVJ3NUWJX4UAMYC/bundle.json","state_url":"https://pith.science/pith/7JOLHEF6LSAXVJ3NUWJX4UAMYC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7JOLHEF6LSAXVJ3NUWJX4UAMYC/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":"2026-08-17T12:35:10Z","links":{"resolver":"https://pith.science/pith/7JOLHEF6LSAXVJ3NUWJX4UAMYC","bundle":"https://pith.science/pith/7JOLHEF6LSAXVJ3NUWJX4UAMYC/bundle.json","state":"https://pith.science/pith/7JOLHEF6LSAXVJ3NUWJX4UAMYC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7JOLHEF6LSAXVJ3NUWJX4UAMYC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7JOLHEF6LSAXVJ3NUWJX4UAMYC","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":"f1ee3b7020f0ffc25939e3d155c1bb2b774ca14216e1cf5a693e3b2f7d59d088","cross_cats_sorted":["cs.CG","cs.NA","math.FA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-21T04:39:48Z","title_canon_sha256":"b21f5bd63ca19f73946901bb8e5f8e35b4ce6e5d1223b4dd62440905ee058b73"},"schema_version":"1.0","source":{"id":"1809.07943","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.07943","created_at":"2026-07-05T00:00:12Z"},{"alias_kind":"arxiv_version","alias_value":"1809.07943v2","created_at":"2026-07-05T00:00:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.07943","created_at":"2026-07-05T00:00:12Z"},{"alias_kind":"pith_short_12","alias_value":"7JOLHEF6LSAX","created_at":"2026-07-05T00:00:12Z"},{"alias_kind":"pith_short_16","alias_value":"7JOLHEF6LSAXVJ3N","created_at":"2026-07-05T00:00:12Z"},{"alias_kind":"pith_short_8","alias_value":"7JOLHEF6","created_at":"2026-07-05T00:00:12Z"}],"graph_snapshots":[{"event_id":"sha256:04c97d768ea1c0a3b10f3fe7293f20924b9efc06ce8298578d2c6cc36e9872db","target":"graph","created_at":"2026-07-05T00:00:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1809.07943/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Applications such as political redistricting demand quantitative measures of geometric compactness to distinguish between simple and contorted shapes. While the isoperimetric quotient, or ratio of area to perimeter squared, is commonly used in practice, it is sensitive to noisy data and irrelevant geographic features like coastline. These issues are addressed in theory by the isoperimetric profile, which plots the minimum perimeter needed to inscribe regions of different prescribed areas within the boundary of a shape. Efficient algorithms for computing this profile, however, are not known in ","authors_text":"Daryl DeFord, Hugo Lavenant, Justin Solomon, Zachary Schutzman","cross_cats":["cs.CG","cs.NA","math.FA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-21T04:39:48Z","title":"Total Variation Isoperimetric Profiles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07943","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":"sha256:7d19eec3c8993aee9b78c6ac95eb38e935782c7cea806335e57434be31b62c70","target":"record","created_at":"2026-07-05T00:00:12Z","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":"f1ee3b7020f0ffc25939e3d155c1bb2b774ca14216e1cf5a693e3b2f7d59d088","cross_cats_sorted":["cs.CG","cs.NA","math.FA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-21T04:39:48Z","title_canon_sha256":"b21f5bd63ca19f73946901bb8e5f8e35b4ce6e5d1223b4dd62440905ee058b73"},"schema_version":"1.0","source":{"id":"1809.07943","kind":"arxiv","version":2}},"canonical_sha256":"fa5cb390be5c817aa76da5937e500cc0b0ae8c60fd15819d980dec4172017b61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa5cb390be5c817aa76da5937e500cc0b0ae8c60fd15819d980dec4172017b61","first_computed_at":"2026-07-05T00:00:12.869669Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:00:12.869669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ju6bG0mRzqvuVNGG7SI5dby1egHgU1AHSgr4PzqrrvxhfLKUnh7l1/hhOyJXSVc/MdWf9p8et6oBFnlWDceLDA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:00:12.870145Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.07943","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d19eec3c8993aee9b78c6ac95eb38e935782c7cea806335e57434be31b62c70","sha256:04c97d768ea1c0a3b10f3fe7293f20924b9efc06ce8298578d2c6cc36e9872db"],"state_sha256":"a748a20029d1e9a85ffa2cf59d8e205ab7680295081fb790b383f3105e9b66d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KL46lz68YbK8qBlWHIHa0huG3uspDCoFBYciuI/HV7TWPpbMTGD68FIT6w91y1uJGkZ7Z8945+zLekgvS8gYCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T12:35:10.006367Z","bundle_sha256":"c647dfe4362aadfabf31fdd8a923cb8517934df9fbae7bc1bed3466532eefcc6"}}