{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4O5EC22UYSLNI63TDAPPCWOEOT","short_pith_number":"pith:4O5EC22U","canonical_record":{"source":{"id":"1708.05540","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-18T09:01:41Z","cross_cats_sorted":["math.AG","math.GR"],"title_canon_sha256":"3aa45a987a7216cebe7e43f708de78f75a22a3f0a52d0b5726f38af6b3c72857","abstract_canon_sha256":"85ca9e87c57168f9018f26bb5664fb9c480981dd2ca1ec4e8543152ff251ebc2"},"schema_version":"1.0"},"canonical_sha256":"e3ba416b54c496d47b73181ef159c474e80d832a23cf03500d355c411fc4c07f","source":{"kind":"arxiv","id":"1708.05540","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.05540","created_at":"2026-05-18T00:08:46Z"},{"alias_kind":"arxiv_version","alias_value":"1708.05540v4","created_at":"2026-05-18T00:08:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.05540","created_at":"2026-05-18T00:08:46Z"},{"alias_kind":"pith_short_12","alias_value":"4O5EC22UYSLN","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4O5EC22UYSLNI63T","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4O5EC22U","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4O5EC22UYSLNI63TDAPPCWOEOT","target":"record","payload":{"canonical_record":{"source":{"id":"1708.05540","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-18T09:01:41Z","cross_cats_sorted":["math.AG","math.GR"],"title_canon_sha256":"3aa45a987a7216cebe7e43f708de78f75a22a3f0a52d0b5726f38af6b3c72857","abstract_canon_sha256":"85ca9e87c57168f9018f26bb5664fb9c480981dd2ca1ec4e8543152ff251ebc2"},"schema_version":"1.0"},"canonical_sha256":"e3ba416b54c496d47b73181ef159c474e80d832a23cf03500d355c411fc4c07f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:46.381566Z","signature_b64":"/7d2B6/wnoIfW1PB9qZ0/+QXSNXNFh5yxoqv5NiEF1weD5fNWc7DUgy22Zkkv88lW5Alz6PDRUtCp9y1cDkPBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3ba416b54c496d47b73181ef159c474e80d832a23cf03500d355c411fc4c07f","last_reissued_at":"2026-05-18T00:08:46.380992Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:46.380992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.05540","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":"2026-05-18T00:08:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZQxx8oCHphNQ4+YlNo1VkCj8n0qqOIuEYf04NDHVDw6EUfMXXMJuaac25LcOrCG/foWVQAiPoYSD6bn6CEVECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:52:36.725388Z"},"content_sha256":"412750deeca59db031253b8e04c2fb651e51cff47553f57358bff902a2656bf5","schema_version":"1.0","event_id":"sha256:412750deeca59db031253b8e04c2fb651e51cff47553f57358bff902a2656bf5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4O5EC22UYSLNI63TDAPPCWOEOT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Automorphisms of even unimodular lattices and equivariant Witt groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.GR"],"primary_cat":"math.NT","authors_text":"Eva Bayer-Fluckiger, Lenny Taelman","submitted_at":"2017-08-18T09:01:41Z","abstract_excerpt":"We characterize the irreducible polynomials that occur as a characteristic polynomial of an automorphism of an even unimodular lattice of given signature, generalizing a theorem of Gross and McMullen. As part of the proof, we give a general criterion in terms of Witt groups for a bilinear form equipped with an action of a group G over a discretely valued field to contain a unimodular G-stable lattice."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05540","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":"2026-05-18T00:08:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Eogzw1/JBIrLmzD/e2WzVGSWySAeakG0wLVYY5+pwZRUjfe2VplTdkr32uXNzV1fZ5gE8maPOkrUvsfTAP57Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:52:36.726117Z"},"content_sha256":"a39eb01cb0857dd79fc6c5aa83c31d2841f23c4c76e3bb1c7c6458b8c79c3d7b","schema_version":"1.0","event_id":"sha256:a39eb01cb0857dd79fc6c5aa83c31d2841f23c4c76e3bb1c7c6458b8c79c3d7b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4O5EC22UYSLNI63TDAPPCWOEOT/bundle.json","state_url":"https://pith.science/pith/4O5EC22UYSLNI63TDAPPCWOEOT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4O5EC22UYSLNI63TDAPPCWOEOT/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":"2026-05-31T23:52:36Z","links":{"resolver":"https://pith.science/pith/4O5EC22UYSLNI63TDAPPCWOEOT","bundle":"https://pith.science/pith/4O5EC22UYSLNI63TDAPPCWOEOT/bundle.json","state":"https://pith.science/pith/4O5EC22UYSLNI63TDAPPCWOEOT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4O5EC22UYSLNI63TDAPPCWOEOT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4O5EC22UYSLNI63TDAPPCWOEOT","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":"85ca9e87c57168f9018f26bb5664fb9c480981dd2ca1ec4e8543152ff251ebc2","cross_cats_sorted":["math.AG","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-18T09:01:41Z","title_canon_sha256":"3aa45a987a7216cebe7e43f708de78f75a22a3f0a52d0b5726f38af6b3c72857"},"schema_version":"1.0","source":{"id":"1708.05540","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.05540","created_at":"2026-05-18T00:08:46Z"},{"alias_kind":"arxiv_version","alias_value":"1708.05540v4","created_at":"2026-05-18T00:08:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.05540","created_at":"2026-05-18T00:08:46Z"},{"alias_kind":"pith_short_12","alias_value":"4O5EC22UYSLN","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4O5EC22UYSLNI63T","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4O5EC22U","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:a39eb01cb0857dd79fc6c5aa83c31d2841f23c4c76e3bb1c7c6458b8c79c3d7b","target":"graph","created_at":"2026-05-18T00:08:46Z","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 characterize the irreducible polynomials that occur as a characteristic polynomial of an automorphism of an even unimodular lattice of given signature, generalizing a theorem of Gross and McMullen. As part of the proof, we give a general criterion in terms of Witt groups for a bilinear form equipped with an action of a group G over a discretely valued field to contain a unimodular G-stable lattice.","authors_text":"Eva Bayer-Fluckiger, Lenny Taelman","cross_cats":["math.AG","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-18T09:01:41Z","title":"Automorphisms of even unimodular lattices and equivariant Witt groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05540","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":"sha256:412750deeca59db031253b8e04c2fb651e51cff47553f57358bff902a2656bf5","target":"record","created_at":"2026-05-18T00:08:46Z","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":"85ca9e87c57168f9018f26bb5664fb9c480981dd2ca1ec4e8543152ff251ebc2","cross_cats_sorted":["math.AG","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-18T09:01:41Z","title_canon_sha256":"3aa45a987a7216cebe7e43f708de78f75a22a3f0a52d0b5726f38af6b3c72857"},"schema_version":"1.0","source":{"id":"1708.05540","kind":"arxiv","version":4}},"canonical_sha256":"e3ba416b54c496d47b73181ef159c474e80d832a23cf03500d355c411fc4c07f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3ba416b54c496d47b73181ef159c474e80d832a23cf03500d355c411fc4c07f","first_computed_at":"2026-05-18T00:08:46.380992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:46.380992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/7d2B6/wnoIfW1PB9qZ0/+QXSNXNFh5yxoqv5NiEF1weD5fNWc7DUgy22Zkkv88lW5Alz6PDRUtCp9y1cDkPBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:46.381566Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.05540","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:412750deeca59db031253b8e04c2fb651e51cff47553f57358bff902a2656bf5","sha256:a39eb01cb0857dd79fc6c5aa83c31d2841f23c4c76e3bb1c7c6458b8c79c3d7b"],"state_sha256":"9852b01b685865f732ca417114e59ca358bf6170fa6d814020a904ff3e08550c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h6SX0ZzQ1n3mbOXXZiDEtpN3G2xbvPFHWq3VKVsXBsOjVXNqSG2pyurjQ0YcMU7m1NUSrumwkdCxZW9YVmWXDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T23:52:36.730399Z","bundle_sha256":"d1828fe086a61198adf353931c1f2e5dc53999d58a757bcf3acdeb6eb384389b"}}