{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NGEBXCE4YSNT3TONS4VODM5N6Y","short_pith_number":"pith:NGEBXCE4","canonical_record":{"source":{"id":"1510.08836","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-29T19:46:18Z","cross_cats_sorted":["math.KT","math.NT"],"title_canon_sha256":"82e139e3777a809f5f13a7bb3a934f61718d67bd5d75f429ab0d4796d8da20d8","abstract_canon_sha256":"ca62dd4f55dd5d1ed5f6a603c2bf9d09e1338f0dc59a0cdb339d48bccf7f8113"},"schema_version":"1.0"},"canonical_sha256":"69881b889cc49b3dcdcd972ae1b3adf621cc4a80dc5aab53927a9769936ea7ad","source":{"kind":"arxiv","id":"1510.08836","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.08836","created_at":"2026-05-18T00:24:31Z"},{"alias_kind":"arxiv_version","alias_value":"1510.08836v3","created_at":"2026-05-18T00:24:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08836","created_at":"2026-05-18T00:24:31Z"},{"alias_kind":"pith_short_12","alias_value":"NGEBXCE4YSNT","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NGEBXCE4YSNT3TON","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NGEBXCE4","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NGEBXCE4YSNT3TONS4VODM5N6Y","target":"record","payload":{"canonical_record":{"source":{"id":"1510.08836","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-29T19:46:18Z","cross_cats_sorted":["math.KT","math.NT"],"title_canon_sha256":"82e139e3777a809f5f13a7bb3a934f61718d67bd5d75f429ab0d4796d8da20d8","abstract_canon_sha256":"ca62dd4f55dd5d1ed5f6a603c2bf9d09e1338f0dc59a0cdb339d48bccf7f8113"},"schema_version":"1.0"},"canonical_sha256":"69881b889cc49b3dcdcd972ae1b3adf621cc4a80dc5aab53927a9769936ea7ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:31.967723Z","signature_b64":"sLYm9L2WCC6lFD1FC8PLvCyKKc22ACvD4ODYSfk5Foa92DMfysnAI7Bx05UqLfbiYic/LWQXq5UJvnyPJ+ffDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69881b889cc49b3dcdcd972ae1b3adf621cc4a80dc5aab53927a9769936ea7ad","last_reissued_at":"2026-05-18T00:24:31.967228Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:31.967228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.08836","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":"2026-05-18T00:24:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h7n97JteLSTH56mmwyKWDISsONpoOFsg0r0J4tZqibnO2UTnqNbu/S2gKIR/rQQEgCre5sryq1ptY0pxpgjODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:03:44.628079Z"},"content_sha256":"e4ddd9e26388c6d0f397f475f4ce7696c60415b71d1431c575c9661fecf3b0db","schema_version":"1.0","event_id":"sha256:e4ddd9e26388c6d0f397f475f4ce7696c60415b71d1431c575c9661fecf3b0db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NGEBXCE4YSNT3TONS4VODM5N6Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Galois action on geometric lattices and the mod-$\\ell$ I/OM","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.NT"],"primary_cat":"math.AG","authors_text":"Adam Topaz","submitted_at":"2015-10-29T19:46:18Z","abstract_excerpt":"This paper studies the Galois action on a special lattice of geometric origin, which is related to mod-$\\ell$ abelian-by-central quotients of geometric fundamental groups of varieties. As a consequence, we formulate and prove the mod-$\\ell$ abelian-by-central variant/strengthening of a conjecture due to Ihara/Oda-Matsumoto."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08836","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":"2026-05-18T00:24:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hn6MkHTEVMy36tAycKubzNrFl2GtVXlgrmEP1bstS4O3x/J5lqBqyXQ+zj1wjY4TWVQaKDdOkWcGoeJ1l9duDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:03:44.628441Z"},"content_sha256":"cfac43ded8ae035bcb9d7c566748750e7208008669db8c407236ad491f264413","schema_version":"1.0","event_id":"sha256:cfac43ded8ae035bcb9d7c566748750e7208008669db8c407236ad491f264413"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NGEBXCE4YSNT3TONS4VODM5N6Y/bundle.json","state_url":"https://pith.science/pith/NGEBXCE4YSNT3TONS4VODM5N6Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NGEBXCE4YSNT3TONS4VODM5N6Y/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":"2026-06-22T16:03:44Z","links":{"resolver":"https://pith.science/pith/NGEBXCE4YSNT3TONS4VODM5N6Y","bundle":"https://pith.science/pith/NGEBXCE4YSNT3TONS4VODM5N6Y/bundle.json","state":"https://pith.science/pith/NGEBXCE4YSNT3TONS4VODM5N6Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NGEBXCE4YSNT3TONS4VODM5N6Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NGEBXCE4YSNT3TONS4VODM5N6Y","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":"ca62dd4f55dd5d1ed5f6a603c2bf9d09e1338f0dc59a0cdb339d48bccf7f8113","cross_cats_sorted":["math.KT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-29T19:46:18Z","title_canon_sha256":"82e139e3777a809f5f13a7bb3a934f61718d67bd5d75f429ab0d4796d8da20d8"},"schema_version":"1.0","source":{"id":"1510.08836","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.08836","created_at":"2026-05-18T00:24:31Z"},{"alias_kind":"arxiv_version","alias_value":"1510.08836v3","created_at":"2026-05-18T00:24:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08836","created_at":"2026-05-18T00:24:31Z"},{"alias_kind":"pith_short_12","alias_value":"NGEBXCE4YSNT","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NGEBXCE4YSNT3TON","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NGEBXCE4","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:cfac43ded8ae035bcb9d7c566748750e7208008669db8c407236ad491f264413","target":"graph","created_at":"2026-05-18T00:24:31Z","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":"This paper studies the Galois action on a special lattice of geometric origin, which is related to mod-$\\ell$ abelian-by-central quotients of geometric fundamental groups of varieties. As a consequence, we formulate and prove the mod-$\\ell$ abelian-by-central variant/strengthening of a conjecture due to Ihara/Oda-Matsumoto.","authors_text":"Adam Topaz","cross_cats":["math.KT","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-29T19:46:18Z","title":"The Galois action on geometric lattices and the mod-$\\ell$ I/OM"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08836","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:e4ddd9e26388c6d0f397f475f4ce7696c60415b71d1431c575c9661fecf3b0db","target":"record","created_at":"2026-05-18T00:24:31Z","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":"ca62dd4f55dd5d1ed5f6a603c2bf9d09e1338f0dc59a0cdb339d48bccf7f8113","cross_cats_sorted":["math.KT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-29T19:46:18Z","title_canon_sha256":"82e139e3777a809f5f13a7bb3a934f61718d67bd5d75f429ab0d4796d8da20d8"},"schema_version":"1.0","source":{"id":"1510.08836","kind":"arxiv","version":3}},"canonical_sha256":"69881b889cc49b3dcdcd972ae1b3adf621cc4a80dc5aab53927a9769936ea7ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69881b889cc49b3dcdcd972ae1b3adf621cc4a80dc5aab53927a9769936ea7ad","first_computed_at":"2026-05-18T00:24:31.967228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:31.967228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sLYm9L2WCC6lFD1FC8PLvCyKKc22ACvD4ODYSfk5Foa92DMfysnAI7Bx05UqLfbiYic/LWQXq5UJvnyPJ+ffDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:31.967723Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.08836","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4ddd9e26388c6d0f397f475f4ce7696c60415b71d1431c575c9661fecf3b0db","sha256:cfac43ded8ae035bcb9d7c566748750e7208008669db8c407236ad491f264413"],"state_sha256":"e98a6eb7ea476f89cd40378a7a75539c79271da5f0fc6fc7f739053ca21b874d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gC/ToaeKM/wVJdS6CWCFV+pL6PPnW+luDo5TGv1p5mbt52eeNs9cM+79DWHo475L9e2T1yNPeirs0nr4vJ4lDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T16:03:44.630269Z","bundle_sha256":"d9ea52b944cc76ff0c900b72d2ad057247b1d933a45b9d7d18a1f8541797177d"}}