{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:CRRQZG3S2VYKUPIKNCOD3CHSCE","short_pith_number":"pith:CRRQZG3S","canonical_record":{"source":{"id":"2312.02955","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2023-12-05T18:40:39Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"f55b8329f5b687d5b128e577942bf0e45dbc74fa49203fc6a8a6cb13d0ebf123","abstract_canon_sha256":"163b0ced466a0cf71e300da187af79e02ba849ad06e075bfa47d35efd10cd7f7"},"schema_version":"1.0"},"canonical_sha256":"14630c9b72d570aa3d0a689c3d88f2112ba78f932a16c8fd15298de4f0596952","source":{"kind":"arxiv","id":"2312.02955","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.02955","created_at":"2026-07-05T07:20:45Z"},{"alias_kind":"arxiv_version","alias_value":"2312.02955v1","created_at":"2026-07-05T07:20:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.02955","created_at":"2026-07-05T07:20:45Z"},{"alias_kind":"pith_short_12","alias_value":"CRRQZG3S2VYK","created_at":"2026-07-05T07:20:45Z"},{"alias_kind":"pith_short_16","alias_value":"CRRQZG3S2VYKUPIK","created_at":"2026-07-05T07:20:45Z"},{"alias_kind":"pith_short_8","alias_value":"CRRQZG3S","created_at":"2026-07-05T07:20:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:CRRQZG3S2VYKUPIKNCOD3CHSCE","target":"record","payload":{"canonical_record":{"source":{"id":"2312.02955","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2023-12-05T18:40:39Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"f55b8329f5b687d5b128e577942bf0e45dbc74fa49203fc6a8a6cb13d0ebf123","abstract_canon_sha256":"163b0ced466a0cf71e300da187af79e02ba849ad06e075bfa47d35efd10cd7f7"},"schema_version":"1.0"},"canonical_sha256":"14630c9b72d570aa3d0a689c3d88f2112ba78f932a16c8fd15298de4f0596952","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:20:45.309488Z","signature_b64":"XxaH0HB0WsRuTrQb7dZD+I/KHk2E5GqOELCcO+xnYwW6jRDgvggcjMIGlto5cfn0YHebkUuxIAhyx+9YwTBeBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14630c9b72d570aa3d0a689c3d88f2112ba78f932a16c8fd15298de4f0596952","last_reissued_at":"2026-07-05T07:20:45.308958Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:20:45.308958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.02955","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:20:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y4pwsMupDJeEtykvK+qXRJkuN6ny5e+uDjoziG5CUT8/H9GqopRnJLLYxK0/ksqLbkeE4SeLpawr0fBBkzYlCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T13:57:23.758380Z"},"content_sha256":"3499fb904702f0cbe6743137eb89f4f638a0f4d1600f6ad617bdac967b1c9624","schema_version":"1.0","event_id":"sha256:3499fb904702f0cbe6743137eb89f4f638a0f4d1600f6ad617bdac967b1c9624"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:CRRQZG3S2VYKUPIKNCOD3CHSCE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Switch Points of Bi-Persistence Matching Distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"cs.CG","authors_text":"Barbara I. Mahler, Celia Hacker, Claudia Landi, Elizabeth R. Stephenson, Robyn Brooks","submitted_at":"2023-12-05T18:40:39Z","abstract_excerpt":"In multi-parameter persistence, the matching distance is defined as the supremum of weighted bottleneck distances on the barcodes given by the restriction of persistence modules to lines with a positive slope. In the case of finitely presented bi-persistence modules, all the available methods to compute the matching distance are based on restricting the computation to lines through pairs from a finite set of points in the plane. Some of these points are determined by the filtration data as they are entrance values of critical simplices. However, these critical values alone are not sufficient f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.02955","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.02955/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":"2026-07-05T07:20:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dRQrgRaJpPUvzRdWJz2OcF/3FfwI3SY1A+5wlQR9unOgG8HpYI14bPBBQPC7L2mYpo50zeXkGRpFcdehx8aJBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T13:57:23.759295Z"},"content_sha256":"017efad6801410b2e41a6f37cc43bc31a7974bfd5d1ebe799bd12b12a1c11c8e","schema_version":"1.0","event_id":"sha256:017efad6801410b2e41a6f37cc43bc31a7974bfd5d1ebe799bd12b12a1c11c8e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CRRQZG3S2VYKUPIKNCOD3CHSCE/bundle.json","state_url":"https://pith.science/pith/CRRQZG3S2VYKUPIKNCOD3CHSCE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CRRQZG3S2VYKUPIKNCOD3CHSCE/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":"2026-08-21T13:57:23Z","links":{"resolver":"https://pith.science/pith/CRRQZG3S2VYKUPIKNCOD3CHSCE","bundle":"https://pith.science/pith/CRRQZG3S2VYKUPIKNCOD3CHSCE/bundle.json","state":"https://pith.science/pith/CRRQZG3S2VYKUPIKNCOD3CHSCE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CRRQZG3S2VYKUPIKNCOD3CHSCE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:CRRQZG3S2VYKUPIKNCOD3CHSCE","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":"163b0ced466a0cf71e300da187af79e02ba849ad06e075bfa47d35efd10cd7f7","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2023-12-05T18:40:39Z","title_canon_sha256":"f55b8329f5b687d5b128e577942bf0e45dbc74fa49203fc6a8a6cb13d0ebf123"},"schema_version":"1.0","source":{"id":"2312.02955","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.02955","created_at":"2026-07-05T07:20:45Z"},{"alias_kind":"arxiv_version","alias_value":"2312.02955v1","created_at":"2026-07-05T07:20:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.02955","created_at":"2026-07-05T07:20:45Z"},{"alias_kind":"pith_short_12","alias_value":"CRRQZG3S2VYK","created_at":"2026-07-05T07:20:45Z"},{"alias_kind":"pith_short_16","alias_value":"CRRQZG3S2VYKUPIK","created_at":"2026-07-05T07:20:45Z"},{"alias_kind":"pith_short_8","alias_value":"CRRQZG3S","created_at":"2026-07-05T07:20:45Z"}],"graph_snapshots":[{"event_id":"sha256:017efad6801410b2e41a6f37cc43bc31a7974bfd5d1ebe799bd12b12a1c11c8e","target":"graph","created_at":"2026-07-05T07:20:45Z","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/2312.02955/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In multi-parameter persistence, the matching distance is defined as the supremum of weighted bottleneck distances on the barcodes given by the restriction of persistence modules to lines with a positive slope. In the case of finitely presented bi-persistence modules, all the available methods to compute the matching distance are based on restricting the computation to lines through pairs from a finite set of points in the plane. Some of these points are determined by the filtration data as they are entrance values of critical simplices. However, these critical values alone are not sufficient f","authors_text":"Barbara I. Mahler, Celia Hacker, Claudia Landi, Elizabeth R. Stephenson, Robyn Brooks","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2023-12-05T18:40:39Z","title":"Switch Points of Bi-Persistence Matching Distance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.02955","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":"sha256:3499fb904702f0cbe6743137eb89f4f638a0f4d1600f6ad617bdac967b1c9624","target":"record","created_at":"2026-07-05T07:20:45Z","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":"163b0ced466a0cf71e300da187af79e02ba849ad06e075bfa47d35efd10cd7f7","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2023-12-05T18:40:39Z","title_canon_sha256":"f55b8329f5b687d5b128e577942bf0e45dbc74fa49203fc6a8a6cb13d0ebf123"},"schema_version":"1.0","source":{"id":"2312.02955","kind":"arxiv","version":1}},"canonical_sha256":"14630c9b72d570aa3d0a689c3d88f2112ba78f932a16c8fd15298de4f0596952","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14630c9b72d570aa3d0a689c3d88f2112ba78f932a16c8fd15298de4f0596952","first_computed_at":"2026-07-05T07:20:45.308958Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:20:45.308958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XxaH0HB0WsRuTrQb7dZD+I/KHk2E5GqOELCcO+xnYwW6jRDgvggcjMIGlto5cfn0YHebkUuxIAhyx+9YwTBeBw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:20:45.309488Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.02955","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3499fb904702f0cbe6743137eb89f4f638a0f4d1600f6ad617bdac967b1c9624","sha256:017efad6801410b2e41a6f37cc43bc31a7974bfd5d1ebe799bd12b12a1c11c8e"],"state_sha256":"85310f7436f0f872c55cc95193e08aee099acf280c0e0c3c581be0cce0c0abe0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PmyRSj3AG7hadfaIskMp2f5ovq6HYzU+bclz3bYpOmHVFDrkv9dGRLomG8kvKS6P0yNMhNqz0db+inbTspVkAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T13:57:23.769968Z","bundle_sha256":"5f6f7bac165006e62695c3743773676ae8b03cf325006fe814a6f12ae849cf7d"}}