{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:5X2KRJJFN2VN3LNARA643ODDJ7","short_pith_number":"pith:5X2KRJJF","canonical_record":{"source":{"id":"1303.0962","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-05T09:33:45Z","cross_cats_sorted":["math.DG","math.GR"],"title_canon_sha256":"d958d5f1ba987b08f36aa26007d8a45dda4f87adc2f5449758e8ebbe9362afa2","abstract_canon_sha256":"be1eb51ed73252945b14b10596be7d87d9d2ea35b66bcdcbbe8b3dd781c0894b"},"schema_version":"1.0"},"canonical_sha256":"edf4a8a5256eaaddada0883dcdb8634ff4fa33c12a72d91f02e7331674f4250f","source":{"kind":"arxiv","id":"1303.0962","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.0962","created_at":"2026-05-18T03:09:12Z"},{"alias_kind":"arxiv_version","alias_value":"1303.0962v3","created_at":"2026-05-18T03:09:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.0962","created_at":"2026-05-18T03:09:12Z"},{"alias_kind":"pith_short_12","alias_value":"5X2KRJJFN2VN","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5X2KRJJFN2VN3LNA","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5X2KRJJF","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:5X2KRJJFN2VN3LNARA643ODDJ7","target":"record","payload":{"canonical_record":{"source":{"id":"1303.0962","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-05T09:33:45Z","cross_cats_sorted":["math.DG","math.GR"],"title_canon_sha256":"d958d5f1ba987b08f36aa26007d8a45dda4f87adc2f5449758e8ebbe9362afa2","abstract_canon_sha256":"be1eb51ed73252945b14b10596be7d87d9d2ea35b66bcdcbbe8b3dd781c0894b"},"schema_version":"1.0"},"canonical_sha256":"edf4a8a5256eaaddada0883dcdb8634ff4fa33c12a72d91f02e7331674f4250f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:12.692919Z","signature_b64":"4Qo/rMsDBq+k8mUqkwgYiY8eTj2dCYFUV4Oir9n0fn5HEmFTet5WQWb7JClWBEtaEZu34lbUJsyU61tnRKvEAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"edf4a8a5256eaaddada0883dcdb8634ff4fa33c12a72d91f02e7331674f4250f","last_reissued_at":"2026-05-18T03:09:12.692375Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:12.692375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.0962","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":"2026-05-18T03:09:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kKsVO6bSSW95rQhBBcRNAUz4tjUHxt9jlszXn/4/fkEYsuQYsbOCtEajx1en5ZPAYSIR1sHWZp4aLHFbkLMJBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:14:58.000412Z"},"content_sha256":"08ef8b97a68c881ec000f07fda38c467671f5a4c93fec43f8bf28765d7337eaf","schema_version":"1.0","event_id":"sha256:08ef8b97a68c881ec000f07fda38c467671f5a4c93fec43f8bf28765d7337eaf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:5X2KRJJFN2VN3LNARA643ODDJ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the vertex-to-edge duality between the Cayley graph and the coset geometry of von Dyck groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GR"],"primary_cat":"math.CO","authors_text":"Giovanni Moreno, Monika Ewa Stypa","submitted_at":"2013-03-05T09:33:45Z","abstract_excerpt":"We prove that the Cayley graph and the coset geometry of the von Dyck group $D(a,b,c)$ are linked by a vertex-to-edge duality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0962","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":"2026-05-18T03:09:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0cpusFrQK0nU6N+NxNoRAdAF/VY2NALgyTzIiTO5K5fbd6N60SCUGBVAL0xd/YZ0tfHT0ObqFeVFFR37vPA6Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:14:58.001047Z"},"content_sha256":"45c3c733bc5a4adfb900d70c7e1d060bff48851de8bc71f8db821b734c4728e1","schema_version":"1.0","event_id":"sha256:45c3c733bc5a4adfb900d70c7e1d060bff48851de8bc71f8db821b734c4728e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5X2KRJJFN2VN3LNARA643ODDJ7/bundle.json","state_url":"https://pith.science/pith/5X2KRJJFN2VN3LNARA643ODDJ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5X2KRJJFN2VN3LNARA643ODDJ7/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":"2026-06-12T09:14:58Z","links":{"resolver":"https://pith.science/pith/5X2KRJJFN2VN3LNARA643ODDJ7","bundle":"https://pith.science/pith/5X2KRJJFN2VN3LNARA643ODDJ7/bundle.json","state":"https://pith.science/pith/5X2KRJJFN2VN3LNARA643ODDJ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5X2KRJJFN2VN3LNARA643ODDJ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5X2KRJJFN2VN3LNARA643ODDJ7","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":"be1eb51ed73252945b14b10596be7d87d9d2ea35b66bcdcbbe8b3dd781c0894b","cross_cats_sorted":["math.DG","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-05T09:33:45Z","title_canon_sha256":"d958d5f1ba987b08f36aa26007d8a45dda4f87adc2f5449758e8ebbe9362afa2"},"schema_version":"1.0","source":{"id":"1303.0962","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.0962","created_at":"2026-05-18T03:09:12Z"},{"alias_kind":"arxiv_version","alias_value":"1303.0962v3","created_at":"2026-05-18T03:09:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.0962","created_at":"2026-05-18T03:09:12Z"},{"alias_kind":"pith_short_12","alias_value":"5X2KRJJFN2VN","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5X2KRJJFN2VN3LNA","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5X2KRJJF","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:45c3c733bc5a4adfb900d70c7e1d060bff48851de8bc71f8db821b734c4728e1","target":"graph","created_at":"2026-05-18T03:09:12Z","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 prove that the Cayley graph and the coset geometry of the von Dyck group $D(a,b,c)$ are linked by a vertex-to-edge duality.","authors_text":"Giovanni Moreno, Monika Ewa Stypa","cross_cats":["math.DG","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-05T09:33:45Z","title":"On the vertex-to-edge duality between the Cayley graph and the coset geometry of von Dyck groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0962","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":"sha256:08ef8b97a68c881ec000f07fda38c467671f5a4c93fec43f8bf28765d7337eaf","target":"record","created_at":"2026-05-18T03:09:12Z","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":"be1eb51ed73252945b14b10596be7d87d9d2ea35b66bcdcbbe8b3dd781c0894b","cross_cats_sorted":["math.DG","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-05T09:33:45Z","title_canon_sha256":"d958d5f1ba987b08f36aa26007d8a45dda4f87adc2f5449758e8ebbe9362afa2"},"schema_version":"1.0","source":{"id":"1303.0962","kind":"arxiv","version":3}},"canonical_sha256":"edf4a8a5256eaaddada0883dcdb8634ff4fa33c12a72d91f02e7331674f4250f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"edf4a8a5256eaaddada0883dcdb8634ff4fa33c12a72d91f02e7331674f4250f","first_computed_at":"2026-05-18T03:09:12.692375Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:12.692375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4Qo/rMsDBq+k8mUqkwgYiY8eTj2dCYFUV4Oir9n0fn5HEmFTet5WQWb7JClWBEtaEZu34lbUJsyU61tnRKvEAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:12.692919Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.0962","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08ef8b97a68c881ec000f07fda38c467671f5a4c93fec43f8bf28765d7337eaf","sha256:45c3c733bc5a4adfb900d70c7e1d060bff48851de8bc71f8db821b734c4728e1"],"state_sha256":"159c884149dc3eca572bd43d0fd58bd4ddae0b3163755c20a896a11e3f51c00f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HpPgv4Dmzq8jvvai/rNGj2vr1nnX8kWARqrN0kLFIOGjZOc9o74vKATaQB6DdfWf4VFLXSxB3V12AEy8iw3LAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T09:14:58.004057Z","bundle_sha256":"4aab8bd492e800d93540867f7ecbb3adcb63d3295bbea51e7b792b78b837e2db"}}