{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:7DX5A2ANM5DQPAG3EKG3WF26IU","short_pith_number":"pith:7DX5A2AN","canonical_record":{"source":{"id":"1301.2001","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-01-09T22:41:38Z","cross_cats_sorted":[],"title_canon_sha256":"c8260de8cb3eea5670c6f0e111821a5464342e77b0a4fdda3fe7694a15afc7cb","abstract_canon_sha256":"2c546787bc21e4e0512df011eda4329cb0bc07fc0af311ca6141e1336f5d89be"},"schema_version":"1.0"},"canonical_sha256":"f8efd0680d67470780db228dbb175e452bdf2c2482fc1fb8d92bb099212fdaf4","source":{"kind":"arxiv","id":"1301.2001","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2001","created_at":"2026-05-18T03:36:48Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2001v1","created_at":"2026-05-18T03:36:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2001","created_at":"2026-05-18T03:36:48Z"},{"alias_kind":"pith_short_12","alias_value":"7DX5A2ANM5DQ","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7DX5A2ANM5DQPAG3","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7DX5A2AN","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:7DX5A2ANM5DQPAG3EKG3WF26IU","target":"record","payload":{"canonical_record":{"source":{"id":"1301.2001","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-01-09T22:41:38Z","cross_cats_sorted":[],"title_canon_sha256":"c8260de8cb3eea5670c6f0e111821a5464342e77b0a4fdda3fe7694a15afc7cb","abstract_canon_sha256":"2c546787bc21e4e0512df011eda4329cb0bc07fc0af311ca6141e1336f5d89be"},"schema_version":"1.0"},"canonical_sha256":"f8efd0680d67470780db228dbb175e452bdf2c2482fc1fb8d92bb099212fdaf4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:48.552535Z","signature_b64":"nCdeW5dlpaNvu07CImLZ6aOJ7bwBVSbcR2yfsJqksQMPSYaeHtXaiyh85x/rtcdKCcoy8JQX2hogZfonM6F8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8efd0680d67470780db228dbb175e452bdf2c2482fc1fb8d92bb099212fdaf4","last_reissued_at":"2026-05-18T03:36:48.552100Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:48.552100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.2001","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:36:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/VmlLmV7Sua0xkVYr99QszM6wNNQrCAjrxrlHzFtBeh0rvV+4cnO5RkLLFNmcYaCh4lL0EvfEXU1I7mIarX7BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:57:49.842353Z"},"content_sha256":"6e3a796202cfb91996373b2b2a83486de69e3b35d6d043fb733c9278cb7f91ab","schema_version":"1.0","event_id":"sha256:6e3a796202cfb91996373b2b2a83486de69e3b35d6d043fb733c9278cb7f91ab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:7DX5A2ANM5DQPAG3EKG3WF26IU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"CSLs of the root lattice $\\mathbf{A_4}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Manuela Heuer, Peter Zeiner","submitted_at":"2013-01-09T22:41:38Z","abstract_excerpt":"Recently, the group of coincidence isometries of the root lattice $A_4$ has been determined providing a classification of these isometries with respect to their coincidence indices. A more difficult task is the classification of all CSLs, since different coincidence isometries may generate the same CSL. In contrast to the typical examples in dimensions $d \\leq 3$, where coincidence isometries generating the same CSL can only differ by a symmetry operation, the situation is more involved in 4 dimensions. Here, we find coincidence isometries that are not related by a symmetry operation but never"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2001","kind":"arxiv","version":1},"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":"2026-05-18T03:36:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YzPcr3BXZ2Y3ULASSBTW2GxhcoBMWgPsQPVpxe0eAnF92CqOKlp7blnm0QwdOfTXnC5e2XMUNrt4a9CIyxeoCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:57:49.842990Z"},"content_sha256":"e82000ff09d8a018dbe64656146a90482815f24a486aa7edda291499f18373b7","schema_version":"1.0","event_id":"sha256:e82000ff09d8a018dbe64656146a90482815f24a486aa7edda291499f18373b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7DX5A2ANM5DQPAG3EKG3WF26IU/bundle.json","state_url":"https://pith.science/pith/7DX5A2ANM5DQPAG3EKG3WF26IU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7DX5A2ANM5DQPAG3EKG3WF26IU/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":"2026-05-31T01:57:49Z","links":{"resolver":"https://pith.science/pith/7DX5A2ANM5DQPAG3EKG3WF26IU","bundle":"https://pith.science/pith/7DX5A2ANM5DQPAG3EKG3WF26IU/bundle.json","state":"https://pith.science/pith/7DX5A2ANM5DQPAG3EKG3WF26IU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7DX5A2ANM5DQPAG3EKG3WF26IU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7DX5A2ANM5DQPAG3EKG3WF26IU","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":"2c546787bc21e4e0512df011eda4329cb0bc07fc0af311ca6141e1336f5d89be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-01-09T22:41:38Z","title_canon_sha256":"c8260de8cb3eea5670c6f0e111821a5464342e77b0a4fdda3fe7694a15afc7cb"},"schema_version":"1.0","source":{"id":"1301.2001","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2001","created_at":"2026-05-18T03:36:48Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2001v1","created_at":"2026-05-18T03:36:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2001","created_at":"2026-05-18T03:36:48Z"},{"alias_kind":"pith_short_12","alias_value":"7DX5A2ANM5DQ","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7DX5A2ANM5DQPAG3","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7DX5A2AN","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:e82000ff09d8a018dbe64656146a90482815f24a486aa7edda291499f18373b7","target":"graph","created_at":"2026-05-18T03:36:48Z","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":"Recently, the group of coincidence isometries of the root lattice $A_4$ has been determined providing a classification of these isometries with respect to their coincidence indices. A more difficult task is the classification of all CSLs, since different coincidence isometries may generate the same CSL. In contrast to the typical examples in dimensions $d \\leq 3$, where coincidence isometries generating the same CSL can only differ by a symmetry operation, the situation is more involved in 4 dimensions. Here, we find coincidence isometries that are not related by a symmetry operation but never","authors_text":"Manuela Heuer, Peter Zeiner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-01-09T22:41:38Z","title":"CSLs of the root lattice $\\mathbf{A_4}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2001","kind":"arxiv","version":1},"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":"sha256:6e3a796202cfb91996373b2b2a83486de69e3b35d6d043fb733c9278cb7f91ab","target":"record","created_at":"2026-05-18T03:36:48Z","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":"2c546787bc21e4e0512df011eda4329cb0bc07fc0af311ca6141e1336f5d89be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-01-09T22:41:38Z","title_canon_sha256":"c8260de8cb3eea5670c6f0e111821a5464342e77b0a4fdda3fe7694a15afc7cb"},"schema_version":"1.0","source":{"id":"1301.2001","kind":"arxiv","version":1}},"canonical_sha256":"f8efd0680d67470780db228dbb175e452bdf2c2482fc1fb8d92bb099212fdaf4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8efd0680d67470780db228dbb175e452bdf2c2482fc1fb8d92bb099212fdaf4","first_computed_at":"2026-05-18T03:36:48.552100Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:48.552100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nCdeW5dlpaNvu07CImLZ6aOJ7bwBVSbcR2yfsJqksQMPSYaeHtXaiyh85x/rtcdKCcoy8JQX2hogZfonM6F8Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:48.552535Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.2001","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e3a796202cfb91996373b2b2a83486de69e3b35d6d043fb733c9278cb7f91ab","sha256:e82000ff09d8a018dbe64656146a90482815f24a486aa7edda291499f18373b7"],"state_sha256":"570d33a1ee2828c1c7809c39bc3d5255cadafd002b204ce91574fdf0fb4d1853"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0ekKa7jlr9xwFurjx9JyleAcMbxk/fIaQgGmoVrHaPVuggZtwjil4PyJMdvL28JOXl6F0R4My159a6vGv3AkCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T01:57:49.845973Z","bundle_sha256":"b0f552875cc46820946bccfe5ebfb22f29c72389ae1e9fde91ffa77db59b8e05"}}