{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ZHCXSXRAJ22EZ3X6CNBAD357VO","short_pith_number":"pith:ZHCXSXRA","canonical_record":{"source":{"id":"1609.00591","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-02T13:28:31Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"2f9bf58dfefd176d3ff6a389cc0f6f5b2dc81ea17b9c54193753bf01c312dae7","abstract_canon_sha256":"528344bc15ea6be361c95d6d1ebd1aa9947e565682831ab20d01399c70a30846"},"schema_version":"1.0"},"canonical_sha256":"c9c5795e204eb44ceefe134201efbfab8b121f0c48bedec0e364e4cec88187e9","source":{"kind":"arxiv","id":"1609.00591","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.00591","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"arxiv_version","alias_value":"1609.00591v1","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00591","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"pith_short_12","alias_value":"ZHCXSXRAJ22E","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZHCXSXRAJ22EZ3X6","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZHCXSXRA","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ZHCXSXRAJ22EZ3X6CNBAD357VO","target":"record","payload":{"canonical_record":{"source":{"id":"1609.00591","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-02T13:28:31Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"2f9bf58dfefd176d3ff6a389cc0f6f5b2dc81ea17b9c54193753bf01c312dae7","abstract_canon_sha256":"528344bc15ea6be361c95d6d1ebd1aa9947e565682831ab20d01399c70a30846"},"schema_version":"1.0"},"canonical_sha256":"c9c5795e204eb44ceefe134201efbfab8b121f0c48bedec0e364e4cec88187e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:23.633266Z","signature_b64":"Po4iWPY94wxXIUL8L5jSUgFJwJAcVIf9DI9/QowltzBI4ifFjRf2hDWVjJZ+IWL+mSCr2ow3TPNx/l6aEJbAAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9c5795e204eb44ceefe134201efbfab8b121f0c48bedec0e364e4cec88187e9","last_reissued_at":"2026-05-18T01:06:23.632799Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:23.632799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.00591","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":"2026-05-18T01:06:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wQEJE/x/6EkwQo2po1HgglV8U0KN2z17wSlGqHHgkKbbPmrdF+4Wy4BwL16Bw9+v7+rQDtt5ke+FTFMT/oUMAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T17:10:47.188560Z"},"content_sha256":"be2dcea851b1171736dbe370d8d8f94a83ea66e4b8941866b946e2b3dd4c44ef","schema_version":"1.0","event_id":"sha256:be2dcea851b1171736dbe370d8d8f94a83ea66e4b8941866b946e2b3dd4c44ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ZHCXSXRAJ22EZ3X6CNBAD357VO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mirror graphs: graph theoretical characterization of reflection arrangements and finite Coxeter groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Tilen Marc","submitted_at":"2016-09-02T13:28:31Z","abstract_excerpt":"Mirror graphs were introduced by Bre\\v{s}ar et al. in 2004 as an intriguing class of graphs: vertex-transitive, isometrically embeddable into hypercubes, having a strong connection with regular maps and polytope structure. In this article we settle the structure of mirror graphs by characterizing them as precisely the Cayley graphs of the finite Coxeter groups or equivalently the tope graphs of reflection arrangements - well understood and classified structures. We provide a polynomial algorithm for their recognition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00591","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":"2026-05-18T01:06:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yOCNDovOzbq4X5r1HC/LrXw/VwMhdLdy0cegg54CBwObKbPWxlW7PVO7XjgqKdXVcJXSZg8GsD2k9bmnwjkXAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T17:10:47.188882Z"},"content_sha256":"e29f69ada41bb87652bc0507274e4b4837ea8a5761c316f71bdb1631f3bcff21","schema_version":"1.0","event_id":"sha256:e29f69ada41bb87652bc0507274e4b4837ea8a5761c316f71bdb1631f3bcff21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZHCXSXRAJ22EZ3X6CNBAD357VO/bundle.json","state_url":"https://pith.science/pith/ZHCXSXRAJ22EZ3X6CNBAD357VO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZHCXSXRAJ22EZ3X6CNBAD357VO/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":"2026-06-25T17:10:47Z","links":{"resolver":"https://pith.science/pith/ZHCXSXRAJ22EZ3X6CNBAD357VO","bundle":"https://pith.science/pith/ZHCXSXRAJ22EZ3X6CNBAD357VO/bundle.json","state":"https://pith.science/pith/ZHCXSXRAJ22EZ3X6CNBAD357VO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZHCXSXRAJ22EZ3X6CNBAD357VO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZHCXSXRAJ22EZ3X6CNBAD357VO","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":"528344bc15ea6be361c95d6d1ebd1aa9947e565682831ab20d01399c70a30846","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-02T13:28:31Z","title_canon_sha256":"2f9bf58dfefd176d3ff6a389cc0f6f5b2dc81ea17b9c54193753bf01c312dae7"},"schema_version":"1.0","source":{"id":"1609.00591","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.00591","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"arxiv_version","alias_value":"1609.00591v1","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00591","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"pith_short_12","alias_value":"ZHCXSXRAJ22E","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZHCXSXRAJ22EZ3X6","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZHCXSXRA","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:e29f69ada41bb87652bc0507274e4b4837ea8a5761c316f71bdb1631f3bcff21","target":"graph","created_at":"2026-05-18T01:06:23Z","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":"Mirror graphs were introduced by Bre\\v{s}ar et al. in 2004 as an intriguing class of graphs: vertex-transitive, isometrically embeddable into hypercubes, having a strong connection with regular maps and polytope structure. In this article we settle the structure of mirror graphs by characterizing them as precisely the Cayley graphs of the finite Coxeter groups or equivalently the tope graphs of reflection arrangements - well understood and classified structures. We provide a polynomial algorithm for their recognition.","authors_text":"Tilen Marc","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-02T13:28:31Z","title":"Mirror graphs: graph theoretical characterization of reflection arrangements and finite Coxeter groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00591","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:be2dcea851b1171736dbe370d8d8f94a83ea66e4b8941866b946e2b3dd4c44ef","target":"record","created_at":"2026-05-18T01:06:23Z","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":"528344bc15ea6be361c95d6d1ebd1aa9947e565682831ab20d01399c70a30846","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-02T13:28:31Z","title_canon_sha256":"2f9bf58dfefd176d3ff6a389cc0f6f5b2dc81ea17b9c54193753bf01c312dae7"},"schema_version":"1.0","source":{"id":"1609.00591","kind":"arxiv","version":1}},"canonical_sha256":"c9c5795e204eb44ceefe134201efbfab8b121f0c48bedec0e364e4cec88187e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9c5795e204eb44ceefe134201efbfab8b121f0c48bedec0e364e4cec88187e9","first_computed_at":"2026-05-18T01:06:23.632799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:23.632799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Po4iWPY94wxXIUL8L5jSUgFJwJAcVIf9DI9/QowltzBI4ifFjRf2hDWVjJZ+IWL+mSCr2ow3TPNx/l6aEJbAAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:23.633266Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.00591","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be2dcea851b1171736dbe370d8d8f94a83ea66e4b8941866b946e2b3dd4c44ef","sha256:e29f69ada41bb87652bc0507274e4b4837ea8a5761c316f71bdb1631f3bcff21"],"state_sha256":"a40ecc6ec40ca6506ec928e905ab3aa988e4b5c70c6f77135e89dd89b3ec750c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DhkcdWbdb0V06mSrYWGLGF1c2afAJz/EO3xcUPo4VzytXbsy/TqV7pubNJlKVR5XojOQGfp8NZZy28x86ecVDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T17:10:47.190686Z","bundle_sha256":"ecf90e31672a31bb3102e84de1cc533007147dac1f9ded2fdb82d709fddcb30b"}}