{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:J23TEXJP6QCF5BKYT2YHJF63ME","short_pith_number":"pith:J23TEXJP","canonical_record":{"source":{"id":"2607.01046","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2026-07-01T15:07:51Z","cross_cats_sorted":["math.DG","math.GT"],"title_canon_sha256":"ca71d70c91a2be25c7d066c6aee790af73fea6ccfb36d4341df51ae9b6578897","abstract_canon_sha256":"89454e836167188c28cf7d681367e18c12d847c4404f0f6c896a3d2cd9f8d204"},"schema_version":"1.0"},"canonical_sha256":"4eb7325d2ff4045e85589eb07497db610e40752af71806e4fb478246b3c04df3","source":{"kind":"arxiv","id":"2607.01046","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01046","created_at":"2026-07-02T01:18:27Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01046v1","created_at":"2026-07-02T01:18:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01046","created_at":"2026-07-02T01:18:27Z"},{"alias_kind":"pith_short_12","alias_value":"J23TEXJP6QCF","created_at":"2026-07-02T01:18:27Z"},{"alias_kind":"pith_short_16","alias_value":"J23TEXJP6QCF5BKY","created_at":"2026-07-02T01:18:27Z"},{"alias_kind":"pith_short_8","alias_value":"J23TEXJP","created_at":"2026-07-02T01:18:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:J23TEXJP6QCF5BKYT2YHJF63ME","target":"record","payload":{"canonical_record":{"source":{"id":"2607.01046","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2026-07-01T15:07:51Z","cross_cats_sorted":["math.DG","math.GT"],"title_canon_sha256":"ca71d70c91a2be25c7d066c6aee790af73fea6ccfb36d4341df51ae9b6578897","abstract_canon_sha256":"89454e836167188c28cf7d681367e18c12d847c4404f0f6c896a3d2cd9f8d204"},"schema_version":"1.0"},"canonical_sha256":"4eb7325d2ff4045e85589eb07497db610e40752af71806e4fb478246b3c04df3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T01:18:27.011727Z","signature_b64":"e3hslQoTUl2UxrLcLvSQRtrJfXHNo/yDL9rpAMWm+CF6lPewdbxiGgiy8jw6Pnj3ccv4QddfjY2GNqNjp6p7BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4eb7325d2ff4045e85589eb07497db610e40752af71806e4fb478246b3c04df3","last_reissued_at":"2026-07-02T01:18:27.011292Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T01:18:27.011292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.01046","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":"2026-07-02T01:18:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eafbC/CR+g8SymRRleORrdrnWlnJ85Gx6vzLANzXmjkqZp8jFCFwlI/Z9MxFFcVyZeYfg1+EeC3sYITd5BB4AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T12:54:18.888270Z"},"content_sha256":"38bd72dfe5440f30ab94d6913ff9aab9d015f26d07429a1e5b7e967efa4ce8a5","schema_version":"1.0","event_id":"sha256:38bd72dfe5440f30ab94d6913ff9aab9d015f26d07429a1e5b7e967efa4ce8a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:J23TEXJP6QCF5BKYT2YHJF63ME","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Singular Source of Vineyard Monodromy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG","math.GT"],"primary_cat":"cs.CG","authors_text":"Christopher Fillmore, Elizabeth Stephenson, Erin W. Chambers, Mathijs Wintraecken, Rohit Roy, Shankha Shubhra Mukherjee","submitted_at":"2026-07-01T15:07:51Z","abstract_excerpt":"Vineyards, or time-varying families of persistence diagrams, are widely used in topological data analysis (TDA) pipelines to track how topological features change and evolve as a parameter varies. When the parameter traces a closed loop, a vineyard can exhibit monodromy: diagram points permute over the course of a full traversal, which obstructs feature tracking and can complicate downstream analysis of such data. Chambers et al. considered the periodic vineyards that arise from the radial persistence transform, which maps the manifold to a family of persistence diagrams, where each diagram fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01046","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/2607.01046/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":"2026-07-02T01:18:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7LpVIgrMM/8OJu1pFHF0G97XYVmL0valOTalHbspDSvjPlnM5TP0F+JgGrpRZcnZ79Xczp2sbA5Tu26FOMdPBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T12:54:18.888659Z"},"content_sha256":"c36e038d21121ceecdc9315970a3ef7fad9665aa40bec12e89716bc1b991eeea","schema_version":"1.0","event_id":"sha256:c36e038d21121ceecdc9315970a3ef7fad9665aa40bec12e89716bc1b991eeea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J23TEXJP6QCF5BKYT2YHJF63ME/bundle.json","state_url":"https://pith.science/pith/J23TEXJP6QCF5BKYT2YHJF63ME/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J23TEXJP6QCF5BKYT2YHJF63ME/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":"2026-07-02T12:54:18Z","links":{"resolver":"https://pith.science/pith/J23TEXJP6QCF5BKYT2YHJF63ME","bundle":"https://pith.science/pith/J23TEXJP6QCF5BKYT2YHJF63ME/bundle.json","state":"https://pith.science/pith/J23TEXJP6QCF5BKYT2YHJF63ME/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J23TEXJP6QCF5BKYT2YHJF63ME/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:J23TEXJP6QCF5BKYT2YHJF63ME","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":"89454e836167188c28cf7d681367e18c12d847c4404f0f6c896a3d2cd9f8d204","cross_cats_sorted":["math.DG","math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2026-07-01T15:07:51Z","title_canon_sha256":"ca71d70c91a2be25c7d066c6aee790af73fea6ccfb36d4341df51ae9b6578897"},"schema_version":"1.0","source":{"id":"2607.01046","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01046","created_at":"2026-07-02T01:18:27Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01046v1","created_at":"2026-07-02T01:18:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01046","created_at":"2026-07-02T01:18:27Z"},{"alias_kind":"pith_short_12","alias_value":"J23TEXJP6QCF","created_at":"2026-07-02T01:18:27Z"},{"alias_kind":"pith_short_16","alias_value":"J23TEXJP6QCF5BKY","created_at":"2026-07-02T01:18:27Z"},{"alias_kind":"pith_short_8","alias_value":"J23TEXJP","created_at":"2026-07-02T01:18:27Z"}],"graph_snapshots":[{"event_id":"sha256:c36e038d21121ceecdc9315970a3ef7fad9665aa40bec12e89716bc1b991eeea","target":"graph","created_at":"2026-07-02T01:18:27Z","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/2607.01046/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Vineyards, or time-varying families of persistence diagrams, are widely used in topological data analysis (TDA) pipelines to track how topological features change and evolve as a parameter varies. When the parameter traces a closed loop, a vineyard can exhibit monodromy: diagram points permute over the course of a full traversal, which obstructs feature tracking and can complicate downstream analysis of such data. Chambers et al. considered the periodic vineyards that arise from the radial persistence transform, which maps the manifold to a family of persistence diagrams, where each diagram fi","authors_text":"Christopher Fillmore, Elizabeth Stephenson, Erin W. Chambers, Mathijs Wintraecken, Rohit Roy, Shankha Shubhra Mukherjee","cross_cats":["math.DG","math.GT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2026-07-01T15:07:51Z","title":"The Singular Source of Vineyard Monodromy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01046","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":"sha256:38bd72dfe5440f30ab94d6913ff9aab9d015f26d07429a1e5b7e967efa4ce8a5","target":"record","created_at":"2026-07-02T01:18:27Z","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":"89454e836167188c28cf7d681367e18c12d847c4404f0f6c896a3d2cd9f8d204","cross_cats_sorted":["math.DG","math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2026-07-01T15:07:51Z","title_canon_sha256":"ca71d70c91a2be25c7d066c6aee790af73fea6ccfb36d4341df51ae9b6578897"},"schema_version":"1.0","source":{"id":"2607.01046","kind":"arxiv","version":1}},"canonical_sha256":"4eb7325d2ff4045e85589eb07497db610e40752af71806e4fb478246b3c04df3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4eb7325d2ff4045e85589eb07497db610e40752af71806e4fb478246b3c04df3","first_computed_at":"2026-07-02T01:18:27.011292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-02T01:18:27.011292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e3hslQoTUl2UxrLcLvSQRtrJfXHNo/yDL9rpAMWm+CF6lPewdbxiGgiy8jw6Pnj3ccv4QddfjY2GNqNjp6p7BA==","signature_status":"signed_v1","signed_at":"2026-07-02T01:18:27.011727Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.01046","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38bd72dfe5440f30ab94d6913ff9aab9d015f26d07429a1e5b7e967efa4ce8a5","sha256:c36e038d21121ceecdc9315970a3ef7fad9665aa40bec12e89716bc1b991eeea"],"state_sha256":"78257acfd599d357a7968bc3c7906e02840cb5ee33d373673aeb80cfee5a5d97"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J97xMVdAqvVIQy/w3tOqcmkY37YF3IIG5fsrP+hEZ+O4AkrmiqkGzp64p8z5DBR0iatCc+rtoMdzP6F+m6awCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T12:54:18.890685Z","bundle_sha256":"6460a5260531aad5bc1435b1dafaeac4a6bcbd437c6b74a8c6c499f3c45d9793"}}