{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:FVKBTALB6G4EV2TRG763KTIZOC","short_pith_number":"pith:FVKBTALB","canonical_record":{"source":{"id":"1311.2084","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-11-08T21:15:34Z","cross_cats_sorted":[],"title_canon_sha256":"bebbc4e9a4a3b1b66e67d77af5342769d4a6e33a9dea73723d23e03ec209a27d","abstract_canon_sha256":"7b1f56247d1016c8563ba02933979d71e8bff52a202710fbc08c0ce7c8edad72"},"schema_version":"1.0"},"canonical_sha256":"2d54198161f1b84aea7137fdb54d19708e6f614e26b5defccb2980fec0cc7c18","source":{"kind":"arxiv","id":"1311.2084","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.2084","created_at":"2026-05-18T01:08:44Z"},{"alias_kind":"arxiv_version","alias_value":"1311.2084v3","created_at":"2026-05-18T01:08:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2084","created_at":"2026-05-18T01:08:44Z"},{"alias_kind":"pith_short_12","alias_value":"FVKBTALB6G4E","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FVKBTALB6G4EV2TR","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FVKBTALB","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:FVKBTALB6G4EV2TRG763KTIZOC","target":"record","payload":{"canonical_record":{"source":{"id":"1311.2084","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-11-08T21:15:34Z","cross_cats_sorted":[],"title_canon_sha256":"bebbc4e9a4a3b1b66e67d77af5342769d4a6e33a9dea73723d23e03ec209a27d","abstract_canon_sha256":"7b1f56247d1016c8563ba02933979d71e8bff52a202710fbc08c0ce7c8edad72"},"schema_version":"1.0"},"canonical_sha256":"2d54198161f1b84aea7137fdb54d19708e6f614e26b5defccb2980fec0cc7c18","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:44.959236Z","signature_b64":"GR2XKcv99QzxD5Dr0Nuyz9O+ZeRY6NXSKYuAFozG0e+OXY7KMTPj64AjCJGWjyVMlM3ZfkPsAE0Xi0MsfCR/BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d54198161f1b84aea7137fdb54d19708e6f614e26b5defccb2980fec0cc7c18","last_reissued_at":"2026-05-18T01:08:44.958838Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:44.958838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.2084","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:08:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jBFyMQyolK7WQB/X9V30jwAQdDFo7VMfHu6+oFVdmxkSG9Hpx1DUKcQXcKlgzD6I2p2cGNFaNaweWvOKC/gJAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:54:43.696631Z"},"content_sha256":"11d5faeeaaca9b1d3e65eeadedfc71655316e02847a7b42ae67a4cf02820a258","schema_version":"1.0","event_id":"sha256:11d5faeeaaca9b1d3e65eeadedfc71655316e02847a7b42ae67a4cf02820a258"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:FVKBTALB6G4EV2TRG763KTIZOC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cubulating hyperbolic free-by-cyclic groups: the irreducible case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Daniel T. Wise, Mark F. Hagen","submitted_at":"2013-11-08T21:15:34Z","abstract_excerpt":"Let $V$ be a finite graph and let $\\phi:V\\rightarrow V$ be an irreducible train track map whose mapping torus has word-hyperbolic fundamental group $G$. Then $G$ acts freely and cocompactly on a CAT(0) cube complex."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2084","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T01:08:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1kbj8jNUKyL6eRo0jHrbZYmq6LE/2fX8kS1d/bFKuzQfCMZ5e/fcut+DKtJWxGNecvLQ//VdHFADu6iNuPWQDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:54:43.697259Z"},"content_sha256":"f32879db03349365cfd33d78bd9955db2057cadcce5a72cc653e000369312311","schema_version":"1.0","event_id":"sha256:f32879db03349365cfd33d78bd9955db2057cadcce5a72cc653e000369312311"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FVKBTALB6G4EV2TRG763KTIZOC/bundle.json","state_url":"https://pith.science/pith/FVKBTALB6G4EV2TRG763KTIZOC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FVKBTALB6G4EV2TRG763KTIZOC/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":"2026-06-07T17:54:43Z","links":{"resolver":"https://pith.science/pith/FVKBTALB6G4EV2TRG763KTIZOC","bundle":"https://pith.science/pith/FVKBTALB6G4EV2TRG763KTIZOC/bundle.json","state":"https://pith.science/pith/FVKBTALB6G4EV2TRG763KTIZOC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FVKBTALB6G4EV2TRG763KTIZOC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FVKBTALB6G4EV2TRG763KTIZOC","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":"7b1f56247d1016c8563ba02933979d71e8bff52a202710fbc08c0ce7c8edad72","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-11-08T21:15:34Z","title_canon_sha256":"bebbc4e9a4a3b1b66e67d77af5342769d4a6e33a9dea73723d23e03ec209a27d"},"schema_version":"1.0","source":{"id":"1311.2084","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.2084","created_at":"2026-05-18T01:08:44Z"},{"alias_kind":"arxiv_version","alias_value":"1311.2084v3","created_at":"2026-05-18T01:08:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2084","created_at":"2026-05-18T01:08:44Z"},{"alias_kind":"pith_short_12","alias_value":"FVKBTALB6G4E","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FVKBTALB6G4EV2TR","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FVKBTALB","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:f32879db03349365cfd33d78bd9955db2057cadcce5a72cc653e000369312311","target":"graph","created_at":"2026-05-18T01:08:44Z","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"},"paper":{"abstract_excerpt":"Let $V$ be a finite graph and let $\\phi:V\\rightarrow V$ be an irreducible train track map whose mapping torus has word-hyperbolic fundamental group $G$. Then $G$ acts freely and cocompactly on a CAT(0) cube complex.","authors_text":"Daniel T. Wise, Mark F. Hagen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-11-08T21:15:34Z","title":"Cubulating hyperbolic free-by-cyclic groups: the irreducible case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2084","kind":"arxiv","version":3},"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":"sha256:11d5faeeaaca9b1d3e65eeadedfc71655316e02847a7b42ae67a4cf02820a258","target":"record","created_at":"2026-05-18T01:08:44Z","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":"7b1f56247d1016c8563ba02933979d71e8bff52a202710fbc08c0ce7c8edad72","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-11-08T21:15:34Z","title_canon_sha256":"bebbc4e9a4a3b1b66e67d77af5342769d4a6e33a9dea73723d23e03ec209a27d"},"schema_version":"1.0","source":{"id":"1311.2084","kind":"arxiv","version":3}},"canonical_sha256":"2d54198161f1b84aea7137fdb54d19708e6f614e26b5defccb2980fec0cc7c18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d54198161f1b84aea7137fdb54d19708e6f614e26b5defccb2980fec0cc7c18","first_computed_at":"2026-05-18T01:08:44.958838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:44.958838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GR2XKcv99QzxD5Dr0Nuyz9O+ZeRY6NXSKYuAFozG0e+OXY7KMTPj64AjCJGWjyVMlM3ZfkPsAE0Xi0MsfCR/BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:44.959236Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.2084","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11d5faeeaaca9b1d3e65eeadedfc71655316e02847a7b42ae67a4cf02820a258","sha256:f32879db03349365cfd33d78bd9955db2057cadcce5a72cc653e000369312311"],"state_sha256":"6ae2280a7eafc84ee5ec726db7f9359e0d64ae071bafabc9a03641029e6f2532"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x8ZG3yyREsIgv0yxeicmY+pGLAk8E9ZcWmZal9y60n0jnLo/uAndUu5GSfXxgALneXgMHM611Zi4S+f0xKfZCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T17:54:43.701017Z","bundle_sha256":"73d4dd3597bbce559344834829772f9e3b34a399726efdc57235f57d58d4de48"}}