{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:FP2SD4XERRMKXPF7RLZYFSABKF","short_pith_number":"pith:FP2SD4XE","canonical_record":{"source":{"id":"2501.08745","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2025-01-15T12:01:41Z","cross_cats_sorted":["cs.CG","math.GN","stat.ML"],"title_canon_sha256":"df5d06662a7d8adcf0394fd8e3dd12479b38b1973e54b2f7e7cf53daa049f38f","abstract_canon_sha256":"6b202fe00ee7da53931e9151b48c7a221b9ac70611817af26a6b6b6047b823fa"},"schema_version":"1.0"},"canonical_sha256":"2bf521f2e48c58abbcbf8af382c8015178f85e6b31f18d036c37faec1cc45f8f","source":{"kind":"arxiv","id":"2501.08745","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.08745","created_at":"2026-07-05T10:05:16Z"},{"alias_kind":"arxiv_version","alias_value":"2501.08745v2","created_at":"2026-07-05T10:05:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.08745","created_at":"2026-07-05T10:05:16Z"},{"alias_kind":"pith_short_12","alias_value":"FP2SD4XERRMK","created_at":"2026-07-05T10:05:16Z"},{"alias_kind":"pith_short_16","alias_value":"FP2SD4XERRMKXPF7","created_at":"2026-07-05T10:05:16Z"},{"alias_kind":"pith_short_8","alias_value":"FP2SD4XE","created_at":"2026-07-05T10:05:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:FP2SD4XERRMKXPF7RLZYFSABKF","target":"record","payload":{"canonical_record":{"source":{"id":"2501.08745","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2025-01-15T12:01:41Z","cross_cats_sorted":["cs.CG","math.GN","stat.ML"],"title_canon_sha256":"df5d06662a7d8adcf0394fd8e3dd12479b38b1973e54b2f7e7cf53daa049f38f","abstract_canon_sha256":"6b202fe00ee7da53931e9151b48c7a221b9ac70611817af26a6b6b6047b823fa"},"schema_version":"1.0"},"canonical_sha256":"2bf521f2e48c58abbcbf8af382c8015178f85e6b31f18d036c37faec1cc45f8f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:05:16.423256Z","signature_b64":"FsXRPeTdKg+M2kOYGZHdaMSAeucsvqWeScAW2EIvkquxbZ/cPOfrP50W5vTD/sChtQAhKm2aH3DcWg0OTvSHAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2bf521f2e48c58abbcbf8af382c8015178f85e6b31f18d036c37faec1cc45f8f","last_reissued_at":"2026-07-05T10:05:16.422774Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:05:16.422774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.08745","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":"2026-07-05T10:05:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"idSddraYgyd8ZO7U6qnfwJvIXIBc0aw+XtD0RqxAFHgeeoeWO8LdNJ4VPSyf/XTvTbiZLK8WX/JjxofTs5hCBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T08:47:50.134210Z"},"content_sha256":"c66e5c802a01c4e9c9ad0fc1823104884be8f54c78a93be4487340e9f0dff50e","schema_version":"1.0","event_id":"sha256:c66e5c802a01c4e9c9ad0fc1823104884be8f54c78a93be4487340e9f0dff50e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:FP2SD4XERRMKXPF7RLZYFSABKF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Is magnitude 'generically continuous' for finite metric spaces?","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG","math.GN","stat.ML"],"primary_cat":"math.MG","authors_text":"Emily Roff, Hirokazu Katsumasa, Masahiko Yoshinaga","submitted_at":"2025-01-15T12:01:41Z","abstract_excerpt":"Magnitude is a real-valued invariant of metric spaces which, in the finite setting, can be understood as recording the 'effective number of points' in a space as the scale of the metric varies. Motivated by applications in topological data analysis, this paper investigates the stability of magnitude: its continuity properties with respect to the Gromov-Hausdorff topology. We show that magnitude is nowhere continuous on the Gromov-Hausdorff space of finite metric spaces. Yet, we find evidence to suggest that it may be 'generically continuous', in the sense that generic Gromov-Hausdorff limits a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.08745","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/2501.08745/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":"2026-07-05T10:05:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F+MhyIsk9JaLXhq6VIc88fVl5cG2NgLxtfOjpta8g0j3DR1W2a8rC9oWuLy5EpBMKO0bjtIWU1eh1bH1+AOSBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T08:47:50.134703Z"},"content_sha256":"8f20fe6cab573e28b06f5e84a874f8601ee5a1f3a2c1fa855cd16e0b694cc493","schema_version":"1.0","event_id":"sha256:8f20fe6cab573e28b06f5e84a874f8601ee5a1f3a2c1fa855cd16e0b694cc493"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FP2SD4XERRMKXPF7RLZYFSABKF/bundle.json","state_url":"https://pith.science/pith/FP2SD4XERRMKXPF7RLZYFSABKF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FP2SD4XERRMKXPF7RLZYFSABKF/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":"2026-08-04T08:47:50Z","links":{"resolver":"https://pith.science/pith/FP2SD4XERRMKXPF7RLZYFSABKF","bundle":"https://pith.science/pith/FP2SD4XERRMKXPF7RLZYFSABKF/bundle.json","state":"https://pith.science/pith/FP2SD4XERRMKXPF7RLZYFSABKF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FP2SD4XERRMKXPF7RLZYFSABKF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FP2SD4XERRMKXPF7RLZYFSABKF","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":"6b202fe00ee7da53931e9151b48c7a221b9ac70611817af26a6b6b6047b823fa","cross_cats_sorted":["cs.CG","math.GN","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2025-01-15T12:01:41Z","title_canon_sha256":"df5d06662a7d8adcf0394fd8e3dd12479b38b1973e54b2f7e7cf53daa049f38f"},"schema_version":"1.0","source":{"id":"2501.08745","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.08745","created_at":"2026-07-05T10:05:16Z"},{"alias_kind":"arxiv_version","alias_value":"2501.08745v2","created_at":"2026-07-05T10:05:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.08745","created_at":"2026-07-05T10:05:16Z"},{"alias_kind":"pith_short_12","alias_value":"FP2SD4XERRMK","created_at":"2026-07-05T10:05:16Z"},{"alias_kind":"pith_short_16","alias_value":"FP2SD4XERRMKXPF7","created_at":"2026-07-05T10:05:16Z"},{"alias_kind":"pith_short_8","alias_value":"FP2SD4XE","created_at":"2026-07-05T10:05:16Z"}],"graph_snapshots":[{"event_id":"sha256:8f20fe6cab573e28b06f5e84a874f8601ee5a1f3a2c1fa855cd16e0b694cc493","target":"graph","created_at":"2026-07-05T10:05:16Z","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/2501.08745/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Magnitude is a real-valued invariant of metric spaces which, in the finite setting, can be understood as recording the 'effective number of points' in a space as the scale of the metric varies. Motivated by applications in topological data analysis, this paper investigates the stability of magnitude: its continuity properties with respect to the Gromov-Hausdorff topology. We show that magnitude is nowhere continuous on the Gromov-Hausdorff space of finite metric spaces. Yet, we find evidence to suggest that it may be 'generically continuous', in the sense that generic Gromov-Hausdorff limits a","authors_text":"Emily Roff, Hirokazu Katsumasa, Masahiko Yoshinaga","cross_cats":["cs.CG","math.GN","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2025-01-15T12:01:41Z","title":"Is magnitude 'generically continuous' for finite metric spaces?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.08745","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:c66e5c802a01c4e9c9ad0fc1823104884be8f54c78a93be4487340e9f0dff50e","target":"record","created_at":"2026-07-05T10:05:16Z","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":"6b202fe00ee7da53931e9151b48c7a221b9ac70611817af26a6b6b6047b823fa","cross_cats_sorted":["cs.CG","math.GN","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2025-01-15T12:01:41Z","title_canon_sha256":"df5d06662a7d8adcf0394fd8e3dd12479b38b1973e54b2f7e7cf53daa049f38f"},"schema_version":"1.0","source":{"id":"2501.08745","kind":"arxiv","version":2}},"canonical_sha256":"2bf521f2e48c58abbcbf8af382c8015178f85e6b31f18d036c37faec1cc45f8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2bf521f2e48c58abbcbf8af382c8015178f85e6b31f18d036c37faec1cc45f8f","first_computed_at":"2026-07-05T10:05:16.422774Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:05:16.422774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FsXRPeTdKg+M2kOYGZHdaMSAeucsvqWeScAW2EIvkquxbZ/cPOfrP50W5vTD/sChtQAhKm2aH3DcWg0OTvSHAg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:05:16.423256Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.08745","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c66e5c802a01c4e9c9ad0fc1823104884be8f54c78a93be4487340e9f0dff50e","sha256:8f20fe6cab573e28b06f5e84a874f8601ee5a1f3a2c1fa855cd16e0b694cc493"],"state_sha256":"bfcc5f28201a4c650edbb7b8c7248f88986ae81c6c0c22aeb2eab71859517ec9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OztXFj5eblM1Jt/MG7Uw2fdniowGjg7MPOQ4vVqZRlfwD99y1Sd96aXAtuCblrD6OLqwDukc9WonvbTJ4vkACw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T08:47:50.142376Z","bundle_sha256":"20dcbe7e0cffecb4692424ffc4ea662cb8f298135deb5b181d77f6b392e8c33d"}}