{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:UMXJ2ZNRHVA6G2E73PWTRK62AK","short_pith_number":"pith:UMXJ2ZNR","canonical_record":{"source":{"id":"2503.04507","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.QM","submitted_at":"2025-03-06T14:54:28Z","cross_cats_sorted":["cs.CG","cs.LG"],"title_canon_sha256":"e5d02d965308048d1f5e1c417a7b22c1d57f30b4a2609596a22157d0754bf685","abstract_canon_sha256":"e8ce57cfb20fed000217438169c2dd2e27efb1b09425e1997d9dc2c5ac4d1b35"},"schema_version":"1.0"},"canonical_sha256":"a32e9d65b13d41e3689fdbed38abda02acc05cf9034944d3994852eb7fd81a4c","source":{"kind":"arxiv","id":"2503.04507","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.04507","created_at":"2026-06-19T16:12:13Z"},{"alias_kind":"arxiv_version","alias_value":"2503.04507v2","created_at":"2026-06-19T16:12:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.04507","created_at":"2026-06-19T16:12:13Z"},{"alias_kind":"pith_short_12","alias_value":"UMXJ2ZNRHVA6","created_at":"2026-06-19T16:12:13Z"},{"alias_kind":"pith_short_16","alias_value":"UMXJ2ZNRHVA6G2E7","created_at":"2026-06-19T16:12:13Z"},{"alias_kind":"pith_short_8","alias_value":"UMXJ2ZNR","created_at":"2026-06-19T16:12:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:UMXJ2ZNRHVA6G2E73PWTRK62AK","target":"record","payload":{"canonical_record":{"source":{"id":"2503.04507","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.QM","submitted_at":"2025-03-06T14:54:28Z","cross_cats_sorted":["cs.CG","cs.LG"],"title_canon_sha256":"e5d02d965308048d1f5e1c417a7b22c1d57f30b4a2609596a22157d0754bf685","abstract_canon_sha256":"e8ce57cfb20fed000217438169c2dd2e27efb1b09425e1997d9dc2c5ac4d1b35"},"schema_version":"1.0"},"canonical_sha256":"a32e9d65b13d41e3689fdbed38abda02acc05cf9034944d3994852eb7fd81a4c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:12:13.406695Z","signature_b64":"k7WxMo9/zTnV5HyrSo7c3AzohonfQxdK7QI4hbmyKHgrt5aikW8nmMcWDlPggfMkgBaTlhRDSltWgow50IsuBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a32e9d65b13d41e3689fdbed38abda02acc05cf9034944d3994852eb7fd81a4c","last_reissued_at":"2026-06-19T16:12:13.406301Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:12:13.406301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.04507","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":"2026-06-19T16:12:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6SC4EOF/Go78tSAYk+r4Q8nojsaYJHEwhy2IRw8sAztZ8Kid2utrDOuCcbi4WiOrNN3/XVznZhDdfAjjrxBnAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:00:32.654697Z"},"content_sha256":"5b3a3bf199515a8b36d14f5b0bf4c6c6f6c8fc06cb7b55d47bb12204b3f66eb2","schema_version":"1.0","event_id":"sha256:5b3a3bf199515a8b36d14f5b0bf4c6c6f6c8fc06cb7b55d47bb12204b3f66eb2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:UMXJ2ZNRHVA6G2E73PWTRK62AK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Morse Transform for Discrete Shape Analysis","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG","cs.LG"],"primary_cat":"q-bio.QM","authors_text":"Alexander M. Tanaka, Aras T. Asaad, Richard Cooper, Vidit Nanda","submitted_at":"2025-03-06T14:54:28Z","abstract_excerpt":"The geometry of an object plays a vital role in modulating its interactions with the physical world. It nevertheless remains difficult to describe geometric information numerically for the purposes of statistical inference or classification tasks. Here, we introduce a new topological transform which leverages directional piecewise-linear Morse theory to quantify the geometry of an embedded object by cataloguing critical points across multiple height-functions. The output of this Morse transform records both the heights and the local topological type (peak, trough or saddle) of the critical poi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.04507","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/2503.04507/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":"2026-06-19T16:12:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ErRoUSWDH9hn+8vs8ZNyN0mUqYZaTwi81kwaXgkOoYFO4gtmNMYfSYK8Ny+hCCk+DgRFJUPH5Kq6KYVnZMizAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:00:32.655075Z"},"content_sha256":"a0dfe46bbc942d50e1b1cd17385d394e033c1c74028d5f99912c627a88f9faa2","schema_version":"1.0","event_id":"sha256:a0dfe46bbc942d50e1b1cd17385d394e033c1c74028d5f99912c627a88f9faa2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UMXJ2ZNRHVA6G2E73PWTRK62AK/bundle.json","state_url":"https://pith.science/pith/UMXJ2ZNRHVA6G2E73PWTRK62AK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UMXJ2ZNRHVA6G2E73PWTRK62AK/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":"2026-06-22T21:00:32Z","links":{"resolver":"https://pith.science/pith/UMXJ2ZNRHVA6G2E73PWTRK62AK","bundle":"https://pith.science/pith/UMXJ2ZNRHVA6G2E73PWTRK62AK/bundle.json","state":"https://pith.science/pith/UMXJ2ZNRHVA6G2E73PWTRK62AK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UMXJ2ZNRHVA6G2E73PWTRK62AK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:UMXJ2ZNRHVA6G2E73PWTRK62AK","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":"e8ce57cfb20fed000217438169c2dd2e27efb1b09425e1997d9dc2c5ac4d1b35","cross_cats_sorted":["cs.CG","cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.QM","submitted_at":"2025-03-06T14:54:28Z","title_canon_sha256":"e5d02d965308048d1f5e1c417a7b22c1d57f30b4a2609596a22157d0754bf685"},"schema_version":"1.0","source":{"id":"2503.04507","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.04507","created_at":"2026-06-19T16:12:13Z"},{"alias_kind":"arxiv_version","alias_value":"2503.04507v2","created_at":"2026-06-19T16:12:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.04507","created_at":"2026-06-19T16:12:13Z"},{"alias_kind":"pith_short_12","alias_value":"UMXJ2ZNRHVA6","created_at":"2026-06-19T16:12:13Z"},{"alias_kind":"pith_short_16","alias_value":"UMXJ2ZNRHVA6G2E7","created_at":"2026-06-19T16:12:13Z"},{"alias_kind":"pith_short_8","alias_value":"UMXJ2ZNR","created_at":"2026-06-19T16:12:13Z"}],"graph_snapshots":[{"event_id":"sha256:a0dfe46bbc942d50e1b1cd17385d394e033c1c74028d5f99912c627a88f9faa2","target":"graph","created_at":"2026-06-19T16:12:13Z","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/2503.04507/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The geometry of an object plays a vital role in modulating its interactions with the physical world. It nevertheless remains difficult to describe geometric information numerically for the purposes of statistical inference or classification tasks. Here, we introduce a new topological transform which leverages directional piecewise-linear Morse theory to quantify the geometry of an embedded object by cataloguing critical points across multiple height-functions. The output of this Morse transform records both the heights and the local topological type (peak, trough or saddle) of the critical poi","authors_text":"Alexander M. Tanaka, Aras T. Asaad, Richard Cooper, Vidit Nanda","cross_cats":["cs.CG","cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.QM","submitted_at":"2025-03-06T14:54:28Z","title":"The Morse Transform for Discrete Shape Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.04507","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":"sha256:5b3a3bf199515a8b36d14f5b0bf4c6c6f6c8fc06cb7b55d47bb12204b3f66eb2","target":"record","created_at":"2026-06-19T16:12:13Z","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":"e8ce57cfb20fed000217438169c2dd2e27efb1b09425e1997d9dc2c5ac4d1b35","cross_cats_sorted":["cs.CG","cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.QM","submitted_at":"2025-03-06T14:54:28Z","title_canon_sha256":"e5d02d965308048d1f5e1c417a7b22c1d57f30b4a2609596a22157d0754bf685"},"schema_version":"1.0","source":{"id":"2503.04507","kind":"arxiv","version":2}},"canonical_sha256":"a32e9d65b13d41e3689fdbed38abda02acc05cf9034944d3994852eb7fd81a4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a32e9d65b13d41e3689fdbed38abda02acc05cf9034944d3994852eb7fd81a4c","first_computed_at":"2026-06-19T16:12:13.406301Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:12:13.406301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k7WxMo9/zTnV5HyrSo7c3AzohonfQxdK7QI4hbmyKHgrt5aikW8nmMcWDlPggfMkgBaTlhRDSltWgow50IsuBw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:12:13.406695Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.04507","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b3a3bf199515a8b36d14f5b0bf4c6c6f6c8fc06cb7b55d47bb12204b3f66eb2","sha256:a0dfe46bbc942d50e1b1cd17385d394e033c1c74028d5f99912c627a88f9faa2"],"state_sha256":"fc8d2f956fab6932b904a25d15e344cf6139d3f46901cfc35fd031b0d4e5d293"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wlEZY3Jh9aQtOj6aiVojS8/9thD6cPNPqIrQDEsdU89ho/uXQXoW2eNzqT47VZ4NcSY0hmY5l6Or1RGQDxneAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T21:00:32.657153Z","bundle_sha256":"98f9742be62a2e0297cf4d920af1cbeb5fbb649124f3ed2861c06153510ee15a"}}