{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:VOCMMOP63IAI4MKPA2TMUXP7ZU","short_pith_number":"pith:VOCMMOP6","canonical_record":{"source":{"id":"1612.03644","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-12T12:30:10Z","cross_cats_sorted":[],"title_canon_sha256":"6a8785f62f6e14509b517521399f5fe97e8bc608f8bdbde102d29dd16228edb4","abstract_canon_sha256":"0d99b035e78b0167f7752d58817d020bbb583b2ba7144808785a58da41faa1aa"},"schema_version":"1.0"},"canonical_sha256":"ab84c639feda008e314f06a6ca5dffcd1ad4a8ef16511ae001d8f1ace786bd98","source":{"kind":"arxiv","id":"1612.03644","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.03644","created_at":"2026-05-17T23:55:10Z"},{"alias_kind":"arxiv_version","alias_value":"1612.03644v3","created_at":"2026-05-17T23:55:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03644","created_at":"2026-05-17T23:55:10Z"},{"alias_kind":"pith_short_12","alias_value":"VOCMMOP63IAI","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VOCMMOP63IAI4MKP","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VOCMMOP6","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:VOCMMOP63IAI4MKPA2TMUXP7ZU","target":"record","payload":{"canonical_record":{"source":{"id":"1612.03644","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-12T12:30:10Z","cross_cats_sorted":[],"title_canon_sha256":"6a8785f62f6e14509b517521399f5fe97e8bc608f8bdbde102d29dd16228edb4","abstract_canon_sha256":"0d99b035e78b0167f7752d58817d020bbb583b2ba7144808785a58da41faa1aa"},"schema_version":"1.0"},"canonical_sha256":"ab84c639feda008e314f06a6ca5dffcd1ad4a8ef16511ae001d8f1ace786bd98","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:10.022405Z","signature_b64":"Qq68FrMlsec0Ur8DPBpBVMyQJIdUe91kzdZswedgfrGPBtU/9VxVonvEbdNU2nFLIPV/1759dfccAKy8IiQSCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab84c639feda008e314f06a6ca5dffcd1ad4a8ef16511ae001d8f1ace786bd98","last_reissued_at":"2026-05-17T23:55:10.022024Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:10.022024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.03644","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":"2026-05-17T23:55:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kon89gKghcGpeh0dSr4CFIdDurVitKRsWddcd7kbeBZl6h8oPJXiV8ScQE1a5VZtpbGyDyQtsLDfLHY2+D2OCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T02:05:54.149915Z"},"content_sha256":"0e12890041eb87b772bde119df010532e6934cdfc49a95febbdb97fdf59f82b4","schema_version":"1.0","event_id":"sha256:0e12890041eb87b772bde119df010532e6934cdfc49a95febbdb97fdf59f82b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:VOCMMOP63IAI4MKPA2TMUXP7ZU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equiangular line systems and switching classes containing regular graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gary R. W. Greaves","submitted_at":"2016-12-12T12:30:10Z","abstract_excerpt":"We develop the theory of equiangular lines in Euclidean spaces. Our focus is on the question of when a Seidel matrix having precisely three distinct eigenvalues has a regular graph in its switching class. We make some progress towards an answer to this question by finding some necessary conditions and some sufficient conditions. Furthermore, we show that the cardinality of an equiangular line system in $18$ dimensional Euclidean space is at most $60$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03644","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":"2026-05-17T23:55:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tn7Td5pcl/VSwqz8cPimrUKSxfNLkqQSR+mFMUd/D6oINFcX/zuS6XJ4Kca5yRctryzLE076Ufbgx5ZgIdgCCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T02:05:54.150254Z"},"content_sha256":"a98eb6425c77f83be97ada297f458b16b42859a869be77294adad0e695adee3a","schema_version":"1.0","event_id":"sha256:a98eb6425c77f83be97ada297f458b16b42859a869be77294adad0e695adee3a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VOCMMOP63IAI4MKPA2TMUXP7ZU/bundle.json","state_url":"https://pith.science/pith/VOCMMOP63IAI4MKPA2TMUXP7ZU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VOCMMOP63IAI4MKPA2TMUXP7ZU/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":"2026-06-27T02:05:54Z","links":{"resolver":"https://pith.science/pith/VOCMMOP63IAI4MKPA2TMUXP7ZU","bundle":"https://pith.science/pith/VOCMMOP63IAI4MKPA2TMUXP7ZU/bundle.json","state":"https://pith.science/pith/VOCMMOP63IAI4MKPA2TMUXP7ZU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VOCMMOP63IAI4MKPA2TMUXP7ZU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VOCMMOP63IAI4MKPA2TMUXP7ZU","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":"0d99b035e78b0167f7752d58817d020bbb583b2ba7144808785a58da41faa1aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-12T12:30:10Z","title_canon_sha256":"6a8785f62f6e14509b517521399f5fe97e8bc608f8bdbde102d29dd16228edb4"},"schema_version":"1.0","source":{"id":"1612.03644","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.03644","created_at":"2026-05-17T23:55:10Z"},{"alias_kind":"arxiv_version","alias_value":"1612.03644v3","created_at":"2026-05-17T23:55:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03644","created_at":"2026-05-17T23:55:10Z"},{"alias_kind":"pith_short_12","alias_value":"VOCMMOP63IAI","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VOCMMOP63IAI4MKP","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VOCMMOP6","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:a98eb6425c77f83be97ada297f458b16b42859a869be77294adad0e695adee3a","target":"graph","created_at":"2026-05-17T23:55:10Z","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 develop the theory of equiangular lines in Euclidean spaces. Our focus is on the question of when a Seidel matrix having precisely three distinct eigenvalues has a regular graph in its switching class. We make some progress towards an answer to this question by finding some necessary conditions and some sufficient conditions. Furthermore, we show that the cardinality of an equiangular line system in $18$ dimensional Euclidean space is at most $60$.","authors_text":"Gary R. W. Greaves","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-12T12:30:10Z","title":"Equiangular line systems and switching classes containing regular graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03644","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":"sha256:0e12890041eb87b772bde119df010532e6934cdfc49a95febbdb97fdf59f82b4","target":"record","created_at":"2026-05-17T23:55:10Z","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":"0d99b035e78b0167f7752d58817d020bbb583b2ba7144808785a58da41faa1aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-12T12:30:10Z","title_canon_sha256":"6a8785f62f6e14509b517521399f5fe97e8bc608f8bdbde102d29dd16228edb4"},"schema_version":"1.0","source":{"id":"1612.03644","kind":"arxiv","version":3}},"canonical_sha256":"ab84c639feda008e314f06a6ca5dffcd1ad4a8ef16511ae001d8f1ace786bd98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab84c639feda008e314f06a6ca5dffcd1ad4a8ef16511ae001d8f1ace786bd98","first_computed_at":"2026-05-17T23:55:10.022024Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:10.022024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qq68FrMlsec0Ur8DPBpBVMyQJIdUe91kzdZswedgfrGPBtU/9VxVonvEbdNU2nFLIPV/1759dfccAKy8IiQSCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:10.022405Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.03644","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e12890041eb87b772bde119df010532e6934cdfc49a95febbdb97fdf59f82b4","sha256:a98eb6425c77f83be97ada297f458b16b42859a869be77294adad0e695adee3a"],"state_sha256":"d7f1c05ac99f2fb261bc778c35a9fff9d8745de32f63c4cbbd970650bee6c072"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uQ0cBO2tOR7HoHuoqlQt7sGXW+J5Nbsk7uOOA5Jf1jEBwVH8FNvlKLNuR0uZTxbq7YZPkn+MfhMYD5qH4IE+AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T02:05:54.152205Z","bundle_sha256":"d1ad03396517c159da23fddb33943137efc517e02b39d767127b6a708e5003cc"}}