{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:BLENO4D6WLNWEZPKRTT4SD4LZA","short_pith_number":"pith:BLENO4D6","canonical_record":{"source":{"id":"0806.1015","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2008-06-05T17:13:13Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"16319f1fa02a3beb07f3c67eb82f1b7eaec00143d1110f44bfe3270ae14d80f2","abstract_canon_sha256":"a6a1adf683bfaf12e728ebc23702e0e473d9da664a043093d34347da73fd0776"},"schema_version":"1.0"},"canonical_sha256":"0ac8d7707eb2db6265ea8ce7c90f8bc83c6f580a237a7e001016c549af76b33d","source":{"kind":"arxiv","id":"0806.1015","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.1015","created_at":"2026-05-18T02:38:19Z"},{"alias_kind":"arxiv_version","alias_value":"0806.1015v2","created_at":"2026-05-18T02:38:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.1015","created_at":"2026-05-18T02:38:19Z"},{"alias_kind":"pith_short_12","alias_value":"BLENO4D6WLNW","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"BLENO4D6WLNWEZPK","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"BLENO4D6","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:BLENO4D6WLNWEZPKRTT4SD4LZA","target":"record","payload":{"canonical_record":{"source":{"id":"0806.1015","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2008-06-05T17:13:13Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"16319f1fa02a3beb07f3c67eb82f1b7eaec00143d1110f44bfe3270ae14d80f2","abstract_canon_sha256":"a6a1adf683bfaf12e728ebc23702e0e473d9da664a043093d34347da73fd0776"},"schema_version":"1.0"},"canonical_sha256":"0ac8d7707eb2db6265ea8ce7c90f8bc83c6f580a237a7e001016c549af76b33d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:19.111210Z","signature_b64":"kNpHmJA1aHpZoA6C8NoJex9eHyyEbXDRcUkmER1T5jXht6cArme808juG6cmV/gfMd278btKjivNhXehUQleDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ac8d7707eb2db6265ea8ce7c90f8bc83c6f580a237a7e001016c549af76b33d","last_reissued_at":"2026-05-18T02:38:19.110695Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:19.110695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0806.1015","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":"2026-05-18T02:38:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SDgpU4Iw32KWr1NVH1SpSAVQSCuW+n0TsnkrycL/AB7iGoXzjjpamGMyexja2qTJIBmT/T1yj5yaJ5yrA9sPDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T10:04:09.603843Z"},"content_sha256":"33ba369dbe6e995d525c8eb791c928adde0efac5a53a00893c24297fb38f344c","schema_version":"1.0","event_id":"sha256:33ba369dbe6e995d525c8eb791c928adde0efac5a53a00893c24297fb38f344c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:BLENO4D6WLNWEZPKRTT4SD4LZA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hyperbolic Groups Which Fiber in Infinitely Many Ways","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Antara Mukherjee, TaraLee Mecham","submitted_at":"2008-06-05T17:13:13Z","abstract_excerpt":"We construct examples of free-by-cyclic hyperbolic groups which fiber in infinitely many ways over Z. The construction involves adding a specialized square 2-cell to a non-positively curved, squared 2-complex defined by labeled oriented graphs. The fundamental groups of the resulting complexes are hyperbolic, free-by-cyclic and can be mapped onto Z in infinitely many ways."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.1015","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":""},"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":"2026-05-18T02:38:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+6hzMG0xoXpNZeFU5NyG8QQJvQwuAsZJC+4GfoOpwMeNgcdKWEIIPYXPmBQGM/OukQuGjEjTgpxuDQq+0yFGCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T10:04:09.604181Z"},"content_sha256":"07cf01c46b4000ecd7d979f0af627e2148d27661ea6b97613c0630a8499d9c2a","schema_version":"1.0","event_id":"sha256:07cf01c46b4000ecd7d979f0af627e2148d27661ea6b97613c0630a8499d9c2a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BLENO4D6WLNWEZPKRTT4SD4LZA/bundle.json","state_url":"https://pith.science/pith/BLENO4D6WLNWEZPKRTT4SD4LZA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BLENO4D6WLNWEZPKRTT4SD4LZA/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":"2026-06-25T10:04:09Z","links":{"resolver":"https://pith.science/pith/BLENO4D6WLNWEZPKRTT4SD4LZA","bundle":"https://pith.science/pith/BLENO4D6WLNWEZPKRTT4SD4LZA/bundle.json","state":"https://pith.science/pith/BLENO4D6WLNWEZPKRTT4SD4LZA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BLENO4D6WLNWEZPKRTT4SD4LZA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:BLENO4D6WLNWEZPKRTT4SD4LZA","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":"a6a1adf683bfaf12e728ebc23702e0e473d9da664a043093d34347da73fd0776","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2008-06-05T17:13:13Z","title_canon_sha256":"16319f1fa02a3beb07f3c67eb82f1b7eaec00143d1110f44bfe3270ae14d80f2"},"schema_version":"1.0","source":{"id":"0806.1015","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.1015","created_at":"2026-05-18T02:38:19Z"},{"alias_kind":"arxiv_version","alias_value":"0806.1015v2","created_at":"2026-05-18T02:38:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.1015","created_at":"2026-05-18T02:38:19Z"},{"alias_kind":"pith_short_12","alias_value":"BLENO4D6WLNW","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"BLENO4D6WLNWEZPK","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"BLENO4D6","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:07cf01c46b4000ecd7d979f0af627e2148d27661ea6b97613c0630a8499d9c2a","target":"graph","created_at":"2026-05-18T02:38:19Z","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":"We construct examples of free-by-cyclic hyperbolic groups which fiber in infinitely many ways over Z. The construction involves adding a specialized square 2-cell to a non-positively curved, squared 2-complex defined by labeled oriented graphs. The fundamental groups of the resulting complexes are hyperbolic, free-by-cyclic and can be mapped onto Z in infinitely many ways.","authors_text":"Antara Mukherjee, TaraLee Mecham","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2008-06-05T17:13:13Z","title":"Hyperbolic Groups Which Fiber in Infinitely Many Ways"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.1015","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":"sha256:33ba369dbe6e995d525c8eb791c928adde0efac5a53a00893c24297fb38f344c","target":"record","created_at":"2026-05-18T02:38:19Z","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":"a6a1adf683bfaf12e728ebc23702e0e473d9da664a043093d34347da73fd0776","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2008-06-05T17:13:13Z","title_canon_sha256":"16319f1fa02a3beb07f3c67eb82f1b7eaec00143d1110f44bfe3270ae14d80f2"},"schema_version":"1.0","source":{"id":"0806.1015","kind":"arxiv","version":2}},"canonical_sha256":"0ac8d7707eb2db6265ea8ce7c90f8bc83c6f580a237a7e001016c549af76b33d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ac8d7707eb2db6265ea8ce7c90f8bc83c6f580a237a7e001016c549af76b33d","first_computed_at":"2026-05-18T02:38:19.110695Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:19.110695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kNpHmJA1aHpZoA6C8NoJex9eHyyEbXDRcUkmER1T5jXht6cArme808juG6cmV/gfMd278btKjivNhXehUQleDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:19.111210Z","signed_message":"canonical_sha256_bytes"},"source_id":"0806.1015","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33ba369dbe6e995d525c8eb791c928adde0efac5a53a00893c24297fb38f344c","sha256:07cf01c46b4000ecd7d979f0af627e2148d27661ea6b97613c0630a8499d9c2a"],"state_sha256":"fc89ec7f3ee47f12c84708d385c844e3f76a6afa7b87434c9367d60c1f71b769"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UL6Mix7pmQMnlkb626dCiD2ckrIhD6Mag9PqUFeZkk0IlyqCpytm9qwsrfK22uO5fg+pBfsM5nSEBSW/iC3QCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T10:04:09.606097Z","bundle_sha256":"383f4658fd9a71e063fc24e4cc878595e6c8a6dc815d612af50cef7684ce0b00"}}