{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:JNOOVKZBBB45WV4VENHPWYZOHF","short_pith_number":"pith:JNOOVKZB","canonical_record":{"source":{"id":"2607.27444","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-07-29T20:15:40Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"dc2e5468c521878e44ae0e20a444e43ee7942d7dc3ce4fc3d37743e69924df17","abstract_canon_sha256":"dfd7254e33ccb8598b6dedb3f81738d3e59717603ab2d1dc942e64f13fb41056"},"schema_version":"1.0"},"canonical_sha256":"4b5ceaab210879db5795234efb632e3971ae9c02dc5a4cd1ca6cb061b24a00ca","source":{"kind":"arxiv","id":"2607.27444","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.27444","created_at":"2026-07-31T00:12:11Z"},{"alias_kind":"arxiv_version","alias_value":"2607.27444v1","created_at":"2026-07-31T00:12:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.27444","created_at":"2026-07-31T00:12:11Z"},{"alias_kind":"pith_short_12","alias_value":"JNOOVKZBBB45","created_at":"2026-07-31T00:12:11Z"},{"alias_kind":"pith_short_16","alias_value":"JNOOVKZBBB45WV4V","created_at":"2026-07-31T00:12:11Z"},{"alias_kind":"pith_short_8","alias_value":"JNOOVKZB","created_at":"2026-07-31T00:12:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:JNOOVKZBBB45WV4VENHPWYZOHF","target":"record","payload":{"canonical_record":{"source":{"id":"2607.27444","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-07-29T20:15:40Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"dc2e5468c521878e44ae0e20a444e43ee7942d7dc3ce4fc3d37743e69924df17","abstract_canon_sha256":"dfd7254e33ccb8598b6dedb3f81738d3e59717603ab2d1dc942e64f13fb41056"},"schema_version":"1.0"},"canonical_sha256":"4b5ceaab210879db5795234efb632e3971ae9c02dc5a4cd1ca6cb061b24a00ca","receipt":{"kind":"pith_receipt","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b5ceaab210879db5795234efb632e3971ae9c02dc5a4cd1ca6cb061b24a00ca","last_reissued_at":"2026-07-31T00:12:11.307440Z","signature_status":"unsigned_v0","first_computed_at":"2026-07-31T00:12:11.307440Z"},"source_kind":"arxiv","source_id":"2607.27444","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":"2026-07-31T00:12:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cKjZNbAQnlHnx1rtSvWNc5+AblDwAfv4nkW24fRKcJQsl+Xj1rUh98+9Bp+Krkj7h61hDEvH2kwPrFY3ixlJDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T22:32:43.672259Z"},"content_sha256":"0a1593e23681f20b82907cee425575dbf443ff5312893e81ee5feb4bab046496","schema_version":"1.0","event_id":"sha256:0a1593e23681f20b82907cee425575dbf443ff5312893e81ee5feb4bab046496"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:JNOOVKZBBB45WV4VENHPWYZOHF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimal hypersurfaces of Morse index one","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Matilde Gianocca, Otis Chodosh","submitted_at":"2026-07-29T20:15:40Z","abstract_excerpt":"We prove that a complete, connected, embedded, minimal hypersurface in $\\mathbb{R}^{n+1}$ with finite total curvature and Morse index one is the higher-dimensional catenoid."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27444","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/2607.27444/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":"2026-07-31T00:12:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yPpi779Zh6tgKFj1wrWIblui/giZ0TzRuB97TpTB8eSvID/wCYOt7icyZzhYqMVFQkZyz77I3XLxzv01e5v/CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T22:32:43.672743Z"},"content_sha256":"adc425d42c2e28c68714083925f9f262ea00e342bfaeb3389875e72fc6d98363","schema_version":"1.0","event_id":"sha256:adc425d42c2e28c68714083925f9f262ea00e342bfaeb3389875e72fc6d98363"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JNOOVKZBBB45WV4VENHPWYZOHF/bundle.json","state_url":"https://pith.science/pith/JNOOVKZBBB45WV4VENHPWYZOHF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JNOOVKZBBB45WV4VENHPWYZOHF/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":"2026-08-20T22:32:43Z","links":{"resolver":"https://pith.science/pith/JNOOVKZBBB45WV4VENHPWYZOHF","bundle":"https://pith.science/pith/JNOOVKZBBB45WV4VENHPWYZOHF/bundle.json","state":"https://pith.science/pith/JNOOVKZBBB45WV4VENHPWYZOHF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JNOOVKZBBB45WV4VENHPWYZOHF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:JNOOVKZBBB45WV4VENHPWYZOHF","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":"dfd7254e33ccb8598b6dedb3f81738d3e59717603ab2d1dc942e64f13fb41056","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-07-29T20:15:40Z","title_canon_sha256":"dc2e5468c521878e44ae0e20a444e43ee7942d7dc3ce4fc3d37743e69924df17"},"schema_version":"1.0","source":{"id":"2607.27444","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.27444","created_at":"2026-07-31T00:12:11Z"},{"alias_kind":"arxiv_version","alias_value":"2607.27444v1","created_at":"2026-07-31T00:12:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.27444","created_at":"2026-07-31T00:12:11Z"},{"alias_kind":"pith_short_12","alias_value":"JNOOVKZBBB45","created_at":"2026-07-31T00:12:11Z"},{"alias_kind":"pith_short_16","alias_value":"JNOOVKZBBB45WV4V","created_at":"2026-07-31T00:12:11Z"},{"alias_kind":"pith_short_8","alias_value":"JNOOVKZB","created_at":"2026-07-31T00:12:11Z"}],"graph_snapshots":[{"event_id":"sha256:adc425d42c2e28c68714083925f9f262ea00e342bfaeb3389875e72fc6d98363","target":"graph","created_at":"2026-07-31T00:12:11Z","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/2607.27444/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that a complete, connected, embedded, minimal hypersurface in $\\mathbb{R}^{n+1}$ with finite total curvature and Morse index one is the higher-dimensional catenoid.","authors_text":"Matilde Gianocca, Otis Chodosh","cross_cats":["math.AP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-07-29T20:15:40Z","title":"Minimal hypersurfaces of Morse index one"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27444","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":"sha256:0a1593e23681f20b82907cee425575dbf443ff5312893e81ee5feb4bab046496","target":"record","created_at":"2026-07-31T00:12:11Z","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":"dfd7254e33ccb8598b6dedb3f81738d3e59717603ab2d1dc942e64f13fb41056","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-07-29T20:15:40Z","title_canon_sha256":"dc2e5468c521878e44ae0e20a444e43ee7942d7dc3ce4fc3d37743e69924df17"},"schema_version":"1.0","source":{"id":"2607.27444","kind":"arxiv","version":1}},"canonical_sha256":"4b5ceaab210879db5795234efb632e3971ae9c02dc5a4cd1ca6cb061b24a00ca","receipt":{"builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b5ceaab210879db5795234efb632e3971ae9c02dc5a4cd1ca6cb061b24a00ca","first_computed_at":"2026-07-31T00:12:11.307440Z","kind":"pith_receipt","last_reissued_at":"2026-07-31T00:12:11.307440Z","receipt_version":"0.3","signature_status":"unsigned_v0"},"source_id":"2607.27444","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a1593e23681f20b82907cee425575dbf443ff5312893e81ee5feb4bab046496","sha256:adc425d42c2e28c68714083925f9f262ea00e342bfaeb3389875e72fc6d98363"],"state_sha256":"21eba20b2d3a69d74def3a2300dfa0df2c92f320e32b635779dbf246a533e6e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zEboYheWp6W/3+2vfsCuC8+CsCPUkuI7/EoBbRmQ4XMZbBcjbzCae9aeWrc30lQwAr8aMV1NL6XEkkEzqbaWBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T22:32:43.676368Z","bundle_sha256":"9b0f0971bc0d8a91afca57e1850663101fd5c7c50251bb8c44de778284cd26c0"}}