{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:L6VLVPJQOW3KJYTH44ODHIQ4OF","short_pith_number":"pith:L6VLVPJQ","canonical_record":{"source":{"id":"2607.04530","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-07-05T22:24:51Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"f8a0b10816837673d714dd406c45b1c2d24a64dc042c3528d95b4601a4166e80","abstract_canon_sha256":"ea4f586d19e8ea94c567e164342e6978f633b9971998d41c75c3928f2695625e"},"schema_version":"1.0"},"canonical_sha256":"5faababd3075b6a4e267e71c33a21c7146aad8a46d0e58b1d442806c10f63e55","source":{"kind":"arxiv","id":"2607.04530","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.04530","created_at":"2026-07-07T02:19:23Z"},{"alias_kind":"arxiv_version","alias_value":"2607.04530v1","created_at":"2026-07-07T02:19:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.04530","created_at":"2026-07-07T02:19:23Z"},{"alias_kind":"pith_short_12","alias_value":"L6VLVPJQOW3K","created_at":"2026-07-07T02:19:23Z"},{"alias_kind":"pith_short_16","alias_value":"L6VLVPJQOW3KJYTH","created_at":"2026-07-07T02:19:23Z"},{"alias_kind":"pith_short_8","alias_value":"L6VLVPJQ","created_at":"2026-07-07T02:19:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:L6VLVPJQOW3KJYTH44ODHIQ4OF","target":"record","payload":{"canonical_record":{"source":{"id":"2607.04530","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-07-05T22:24:51Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"f8a0b10816837673d714dd406c45b1c2d24a64dc042c3528d95b4601a4166e80","abstract_canon_sha256":"ea4f586d19e8ea94c567e164342e6978f633b9971998d41c75c3928f2695625e"},"schema_version":"1.0"},"canonical_sha256":"5faababd3075b6a4e267e71c33a21c7146aad8a46d0e58b1d442806c10f63e55","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T02:19:23.397504Z","signature_b64":"8S08aqEeDU9gyTR6UVVNS0rE7EsLvGsN7TUiNySgHxRKWwFgufB/D8u5nxC7wKn/3ekKuhq5qrenEpc+e6JQDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5faababd3075b6a4e267e71c33a21c7146aad8a46d0e58b1d442806c10f63e55","last_reissued_at":"2026-07-07T02:19:23.396755Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T02:19:23.396755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.04530","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":"2026-07-07T02:19:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oNlF1NZwrJOD5xXlv1uiKaA6W0AMGcyvjEYhHss8npxOieC/GDfVtjwYvTcbRCEkYT96pmlMtQABl6Xa4jk0DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T08:39:46.491427Z"},"content_sha256":"42132cba29f0eb69a68336f874d58f407bef6949de530d531e7dd362f4bbc872","schema_version":"1.0","event_id":"sha256:42132cba29f0eb69a68336f874d58f407bef6949de530d531e7dd362f4bbc872"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:L6VLVPJQOW3KJYTH44ODHIQ4OF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularity of profinite isomorphisms of hyperbolic 3-manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Liam Hanany","submitted_at":"2026-07-05T22:24:51Z","abstract_excerpt":"We strengthen a result of Liu from his papers arXiv:2011.09412, arXiv:2105.01022, by proving that profinite isomorphisms of hyperbolic 3-manifolds are regular in the sense of Boileau and Friedl arXiv:1505.07799"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04530","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/2607.04530/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":"2026-07-07T02:19:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eHSFZliz8KPt/DYBre8YDXHObASaXhzwrkd3NOkInjzdhnDAOIeMaTcePDU+rdCjgoz0jwrFsPbYwv90HaWOBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T08:39:46.491932Z"},"content_sha256":"d81dfd94eced8316d21653ad80bd39fe653e8c77f88fd02e76c9df00e1a4747d","schema_version":"1.0","event_id":"sha256:d81dfd94eced8316d21653ad80bd39fe653e8c77f88fd02e76c9df00e1a4747d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L6VLVPJQOW3KJYTH44ODHIQ4OF/bundle.json","state_url":"https://pith.science/pith/L6VLVPJQOW3KJYTH44ODHIQ4OF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L6VLVPJQOW3KJYTH44ODHIQ4OF/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":"2026-08-09T08:39:46Z","links":{"resolver":"https://pith.science/pith/L6VLVPJQOW3KJYTH44ODHIQ4OF","bundle":"https://pith.science/pith/L6VLVPJQOW3KJYTH44ODHIQ4OF/bundle.json","state":"https://pith.science/pith/L6VLVPJQOW3KJYTH44ODHIQ4OF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L6VLVPJQOW3KJYTH44ODHIQ4OF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:L6VLVPJQOW3KJYTH44ODHIQ4OF","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":"ea4f586d19e8ea94c567e164342e6978f633b9971998d41c75c3928f2695625e","cross_cats_sorted":["math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-07-05T22:24:51Z","title_canon_sha256":"f8a0b10816837673d714dd406c45b1c2d24a64dc042c3528d95b4601a4166e80"},"schema_version":"1.0","source":{"id":"2607.04530","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.04530","created_at":"2026-07-07T02:19:23Z"},{"alias_kind":"arxiv_version","alias_value":"2607.04530v1","created_at":"2026-07-07T02:19:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.04530","created_at":"2026-07-07T02:19:23Z"},{"alias_kind":"pith_short_12","alias_value":"L6VLVPJQOW3K","created_at":"2026-07-07T02:19:23Z"},{"alias_kind":"pith_short_16","alias_value":"L6VLVPJQOW3KJYTH","created_at":"2026-07-07T02:19:23Z"},{"alias_kind":"pith_short_8","alias_value":"L6VLVPJQ","created_at":"2026-07-07T02:19:23Z"}],"graph_snapshots":[{"event_id":"sha256:d81dfd94eced8316d21653ad80bd39fe653e8c77f88fd02e76c9df00e1a4747d","target":"graph","created_at":"2026-07-07T02:19:23Z","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/2607.04530/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We strengthen a result of Liu from his papers arXiv:2011.09412, arXiv:2105.01022, by proving that profinite isomorphisms of hyperbolic 3-manifolds are regular in the sense of Boileau and Friedl arXiv:1505.07799","authors_text":"Liam Hanany","cross_cats":["math.GT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-07-05T22:24:51Z","title":"Regularity of profinite isomorphisms of hyperbolic 3-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04530","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":"sha256:42132cba29f0eb69a68336f874d58f407bef6949de530d531e7dd362f4bbc872","target":"record","created_at":"2026-07-07T02:19:23Z","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":"ea4f586d19e8ea94c567e164342e6978f633b9971998d41c75c3928f2695625e","cross_cats_sorted":["math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-07-05T22:24:51Z","title_canon_sha256":"f8a0b10816837673d714dd406c45b1c2d24a64dc042c3528d95b4601a4166e80"},"schema_version":"1.0","source":{"id":"2607.04530","kind":"arxiv","version":1}},"canonical_sha256":"5faababd3075b6a4e267e71c33a21c7146aad8a46d0e58b1d442806c10f63e55","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5faababd3075b6a4e267e71c33a21c7146aad8a46d0e58b1d442806c10f63e55","first_computed_at":"2026-07-07T02:19:23.396755Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T02:19:23.396755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8S08aqEeDU9gyTR6UVVNS0rE7EsLvGsN7TUiNySgHxRKWwFgufB/D8u5nxC7wKn/3ekKuhq5qrenEpc+e6JQDQ==","signature_status":"signed_v1","signed_at":"2026-07-07T02:19:23.397504Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.04530","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42132cba29f0eb69a68336f874d58f407bef6949de530d531e7dd362f4bbc872","sha256:d81dfd94eced8316d21653ad80bd39fe653e8c77f88fd02e76c9df00e1a4747d"],"state_sha256":"42d31cfd76c7b99e4b363910477b921a46d1e530f45b6758449b6a444fdf86c2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AtZDMyjAbl9V7oG3hUwRv6SX5ja9cgoiBeve1o7lxqWdR9VA0oEDVRyMxLp0zFbjYSSa+Je5RDVZmp4aByzqDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T08:39:46.497826Z","bundle_sha256":"057c4995ad5a707019bb6ec3abff3805cf40176a395a8a5a0e2c0a5b2ea89b07"}}