{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:ZU2YOVNJFR3JZ3KEGYARBT6XCG","short_pith_number":"pith:ZU2YOVNJ","canonical_record":{"source":{"id":"math/0506528","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2005-06-26T11:08:51Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"095896f2e6a3a304d00a06607b3edd9bce9d9a33251d2caefa5746712c66d454","abstract_canon_sha256":"dc9f9a2c3a3f1bc06b3d22350e129f7fbedc09ebf410a9d92d80f7b1eaff2437"},"schema_version":"1.0"},"canonical_sha256":"cd358755a92c769ced44360110cfd7119ffa9ed560213a044a5f2e70d566010e","source":{"kind":"arxiv","id":"math/0506528","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0506528","created_at":"2026-05-18T04:23:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0506528v4","created_at":"2026-05-18T04:23:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0506528","created_at":"2026-05-18T04:23:21Z"},{"alias_kind":"pith_short_12","alias_value":"ZU2YOVNJFR3J","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZU2YOVNJFR3JZ3KE","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZU2YOVNJ","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:ZU2YOVNJFR3JZ3KEGYARBT6XCG","target":"record","payload":{"canonical_record":{"source":{"id":"math/0506528","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2005-06-26T11:08:51Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"095896f2e6a3a304d00a06607b3edd9bce9d9a33251d2caefa5746712c66d454","abstract_canon_sha256":"dc9f9a2c3a3f1bc06b3d22350e129f7fbedc09ebf410a9d92d80f7b1eaff2437"},"schema_version":"1.0"},"canonical_sha256":"cd358755a92c769ced44360110cfd7119ffa9ed560213a044a5f2e70d566010e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:21.418632Z","signature_b64":"1w5VIv+0dfYuWa0LqkWvGnAZXEW6N0A6/YoKSPntJTyQ6GPE2h3ROZZfbesg6GbExiga4q+WRD7Z1exUZqL/Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd358755a92c769ced44360110cfd7119ffa9ed560213a044a5f2e70d566010e","last_reissued_at":"2026-05-18T04:23:21.418058Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:21.418058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0506528","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:23:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t6JtvPfC8Mvx/kuMyJPZ4E9/vWQ9uZ4uJBkVCwWxWC9xWhApLo+zEJyq5zzDm/FZE0p/zLyP1gEa4JX1KFi4Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T10:33:56.818378Z"},"content_sha256":"e1b9e6108d652d9b44e159ff7597bab40d1dbaa85c7dd6ddee475fe573839a69","schema_version":"1.0","event_id":"sha256:e1b9e6108d652d9b44e159ff7597bab40d1dbaa85c7dd6ddee475fe573839a69"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:ZU2YOVNJFR3JZ3KEGYARBT6XCG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalizations of Agol's inequality and nonexistence of tight laminations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.GT","authors_text":"Thilo Kuessner","submitted_at":"2005-06-26T11:08:51Z","abstract_excerpt":"We give a general lower bound for the normal Gromov norm of genuine laminations in terms of the topology of the complementary regions.\n  In the special case of 3-manifolds, this yields a generalization of Agol's inequality from incompressible surfaces to tight laminations. In particular, the inequality excludes the existence of tight laminations with nonempty guts on 3-manifolds of small simplicial volume."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506528","kind":"arxiv","version":4},"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":"2026-05-18T04:23:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h7V+ydpTR4v9iOedicuv304Qzdi3WtzT9+r5P3IXdaFUSGomrm+uIPTKlw+EwRcjCuMRMYk5rhCCLquqFn2oCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T10:33:56.818714Z"},"content_sha256":"9e28ba74b293fe42728d7296db817cad9b80b365c08af39fc087ab4c4749317f","schema_version":"1.0","event_id":"sha256:9e28ba74b293fe42728d7296db817cad9b80b365c08af39fc087ab4c4749317f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZU2YOVNJFR3JZ3KEGYARBT6XCG/bundle.json","state_url":"https://pith.science/pith/ZU2YOVNJFR3JZ3KEGYARBT6XCG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZU2YOVNJFR3JZ3KEGYARBT6XCG/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":"2026-06-23T10:33:56Z","links":{"resolver":"https://pith.science/pith/ZU2YOVNJFR3JZ3KEGYARBT6XCG","bundle":"https://pith.science/pith/ZU2YOVNJFR3JZ3KEGYARBT6XCG/bundle.json","state":"https://pith.science/pith/ZU2YOVNJFR3JZ3KEGYARBT6XCG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZU2YOVNJFR3JZ3KEGYARBT6XCG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:ZU2YOVNJFR3JZ3KEGYARBT6XCG","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":"dc9f9a2c3a3f1bc06b3d22350e129f7fbedc09ebf410a9d92d80f7b1eaff2437","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2005-06-26T11:08:51Z","title_canon_sha256":"095896f2e6a3a304d00a06607b3edd9bce9d9a33251d2caefa5746712c66d454"},"schema_version":"1.0","source":{"id":"math/0506528","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0506528","created_at":"2026-05-18T04:23:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0506528v4","created_at":"2026-05-18T04:23:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0506528","created_at":"2026-05-18T04:23:21Z"},{"alias_kind":"pith_short_12","alias_value":"ZU2YOVNJFR3J","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZU2YOVNJFR3JZ3KE","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZU2YOVNJ","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:9e28ba74b293fe42728d7296db817cad9b80b365c08af39fc087ab4c4749317f","target":"graph","created_at":"2026-05-18T04:23:21Z","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 give a general lower bound for the normal Gromov norm of genuine laminations in terms of the topology of the complementary regions.\n  In the special case of 3-manifolds, this yields a generalization of Agol's inequality from incompressible surfaces to tight laminations. In particular, the inequality excludes the existence of tight laminations with nonempty guts on 3-manifolds of small simplicial volume.","authors_text":"Thilo Kuessner","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2005-06-26T11:08:51Z","title":"Generalizations of Agol's inequality and nonexistence of tight laminations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506528","kind":"arxiv","version":4},"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:e1b9e6108d652d9b44e159ff7597bab40d1dbaa85c7dd6ddee475fe573839a69","target":"record","created_at":"2026-05-18T04:23:21Z","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":"dc9f9a2c3a3f1bc06b3d22350e129f7fbedc09ebf410a9d92d80f7b1eaff2437","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2005-06-26T11:08:51Z","title_canon_sha256":"095896f2e6a3a304d00a06607b3edd9bce9d9a33251d2caefa5746712c66d454"},"schema_version":"1.0","source":{"id":"math/0506528","kind":"arxiv","version":4}},"canonical_sha256":"cd358755a92c769ced44360110cfd7119ffa9ed560213a044a5f2e70d566010e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd358755a92c769ced44360110cfd7119ffa9ed560213a044a5f2e70d566010e","first_computed_at":"2026-05-18T04:23:21.418058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:21.418058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1w5VIv+0dfYuWa0LqkWvGnAZXEW6N0A6/YoKSPntJTyQ6GPE2h3ROZZfbesg6GbExiga4q+WRD7Z1exUZqL/Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:21.418632Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0506528","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1b9e6108d652d9b44e159ff7597bab40d1dbaa85c7dd6ddee475fe573839a69","sha256:9e28ba74b293fe42728d7296db817cad9b80b365c08af39fc087ab4c4749317f"],"state_sha256":"47557f3ff78967ce8478673a3efbf2dbf533184d88c5b0f261ded1a404c8fa2a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kiaVNDwBo93Cjq95mfpvprZbcIIQQDxChjHoB7FhhvPIo0fn+dxnWkJTdgl0wx+Tp8Nvbv+hoGaxgqZJAEt8BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T10:33:56.820497Z","bundle_sha256":"c07b7ada6f916133e11d0221943c1fd0f4496df62cd9ec4fdebd833d5cd18e74"}}