{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:FY7GVTEBYA4PJIIWGZV7G2XSGA","short_pith_number":"pith:FY7GVTEB","canonical_record":{"source":{"id":"2511.21144","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-11-26T07:56:46Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"d8b71ee27e660a1bab1eac61b6af46e06eef190d193f07bb8506fff774eb3883","abstract_canon_sha256":"682beb96b92c322557e2cf9676f2f72ca2875048cc4bd7574aed470cde337a8f"},"schema_version":"1.0"},"canonical_sha256":"2e3e6acc81c038f4a116366bf36af23010dea3b4e235cba4b5bc5b5e1d6dc091","source":{"kind":"arxiv","id":"2511.21144","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2511.21144","created_at":"2026-06-29T01:14:26Z"},{"alias_kind":"arxiv_version","alias_value":"2511.21144v2","created_at":"2026-06-29T01:14:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.21144","created_at":"2026-06-29T01:14:26Z"},{"alias_kind":"pith_short_12","alias_value":"FY7GVTEBYA4P","created_at":"2026-06-29T01:14:26Z"},{"alias_kind":"pith_short_16","alias_value":"FY7GVTEBYA4PJIIW","created_at":"2026-06-29T01:14:26Z"},{"alias_kind":"pith_short_8","alias_value":"FY7GVTEB","created_at":"2026-06-29T01:14:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:FY7GVTEBYA4PJIIWGZV7G2XSGA","target":"record","payload":{"canonical_record":{"source":{"id":"2511.21144","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-11-26T07:56:46Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"d8b71ee27e660a1bab1eac61b6af46e06eef190d193f07bb8506fff774eb3883","abstract_canon_sha256":"682beb96b92c322557e2cf9676f2f72ca2875048cc4bd7574aed470cde337a8f"},"schema_version":"1.0"},"canonical_sha256":"2e3e6acc81c038f4a116366bf36af23010dea3b4e235cba4b5bc5b5e1d6dc091","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-29T01:14:26.703777Z","signature_b64":"ERGy8OSeJRzjh3u6pJFMzrDiWZdmitgtc88Z2x7lj5OVztkuVhjisVUJ7eSp8jKfjSMYW2ym9seMwaz9DOXABQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e3e6acc81c038f4a116366bf36af23010dea3b4e235cba4b5bc5b5e1d6dc091","last_reissued_at":"2026-06-29T01:14:26.703299Z","signature_status":"signed_v1","first_computed_at":"2026-06-29T01:14:26.703299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2511.21144","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-29T01:14:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F+/dEC2hoSsLqT8edIymNUmInBxwYdA5k4qD4/aS0wbM5NnbGKtgnfLLzB05ecvmc67TYc7OhSsIXmJdmMM/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T12:44:38.489721Z"},"content_sha256":"6a47fbd040d2f362faa00a55c7dd5489f99cb305cc2cba1c23a02b6e0f6fcb45","schema_version":"1.0","event_id":"sha256:6a47fbd040d2f362faa00a55c7dd5489f99cb305cc2cba1c23a02b6e0f6fcb45"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:FY7GVTEBYA4PJIIWGZV7G2XSGA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the order-diameter ratio of girth-diameter cages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Jan Goedgebeur, Jorik Jooken, Stijn Cambie, Tibo Van den Eede","submitted_at":"2025-11-26T07:56:46Z","abstract_excerpt":"For integers $k,g,d$, a $(k;g,d)$-cage (or simply girth-diameter cage) is a smallest $k$-regular graph of girth $g$ and diameter $d$ (if it exists). The order of a $(k;g,d)$-cage is denoted by $n(k;g,d)$. We determine asymptotic lower and upper bounds for the ratio between the order and the diameter of girth-diameter cages as the diameter goes to infinity. We also prove that this ratio can be computed in constant time for fixed $k$ and $g$.\n  We theoretically determine the exact values $n(3;g,d)$, and count the number of corresponding girth-diameter cages, for $g \\in \\{4,5\\}$. Moreover, we des"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.21144","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2511.21144/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-29T01:14:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"imzSSu2sHShtmeYTjwNe/pKcMbHRxPveFTgFrPahODKva02zmmtJ8rWz3vSaSFsqRnTCMFYfFE5bkk29YuP7Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T12:44:38.490255Z"},"content_sha256":"5f95a48ab23b03c1bd0db5e75f66856bb724e6acc81bedd36a9c911e9b546c7c","schema_version":"1.0","event_id":"sha256:5f95a48ab23b03c1bd0db5e75f66856bb724e6acc81bedd36a9c911e9b546c7c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FY7GVTEBYA4PJIIWGZV7G2XSGA/bundle.json","state_url":"https://pith.science/pith/FY7GVTEBYA4PJIIWGZV7G2XSGA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FY7GVTEBYA4PJIIWGZV7G2XSGA/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":"2026-08-09T12:44:38Z","links":{"resolver":"https://pith.science/pith/FY7GVTEBYA4PJIIWGZV7G2XSGA","bundle":"https://pith.science/pith/FY7GVTEBYA4PJIIWGZV7G2XSGA/bundle.json","state":"https://pith.science/pith/FY7GVTEBYA4PJIIWGZV7G2XSGA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FY7GVTEBYA4PJIIWGZV7G2XSGA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FY7GVTEBYA4PJIIWGZV7G2XSGA","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":"682beb96b92c322557e2cf9676f2f72ca2875048cc4bd7574aed470cde337a8f","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-11-26T07:56:46Z","title_canon_sha256":"d8b71ee27e660a1bab1eac61b6af46e06eef190d193f07bb8506fff774eb3883"},"schema_version":"1.0","source":{"id":"2511.21144","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2511.21144","created_at":"2026-06-29T01:14:26Z"},{"alias_kind":"arxiv_version","alias_value":"2511.21144v2","created_at":"2026-06-29T01:14:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.21144","created_at":"2026-06-29T01:14:26Z"},{"alias_kind":"pith_short_12","alias_value":"FY7GVTEBYA4P","created_at":"2026-06-29T01:14:26Z"},{"alias_kind":"pith_short_16","alias_value":"FY7GVTEBYA4PJIIW","created_at":"2026-06-29T01:14:26Z"},{"alias_kind":"pith_short_8","alias_value":"FY7GVTEB","created_at":"2026-06-29T01:14:26Z"}],"graph_snapshots":[{"event_id":"sha256:5f95a48ab23b03c1bd0db5e75f66856bb724e6acc81bedd36a9c911e9b546c7c","target":"graph","created_at":"2026-06-29T01:14:26Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2511.21144/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For integers $k,g,d$, a $(k;g,d)$-cage (or simply girth-diameter cage) is a smallest $k$-regular graph of girth $g$ and diameter $d$ (if it exists). The order of a $(k;g,d)$-cage is denoted by $n(k;g,d)$. We determine asymptotic lower and upper bounds for the ratio between the order and the diameter of girth-diameter cages as the diameter goes to infinity. We also prove that this ratio can be computed in constant time for fixed $k$ and $g$.\n  We theoretically determine the exact values $n(3;g,d)$, and count the number of corresponding girth-diameter cages, for $g \\in \\{4,5\\}$. Moreover, we des","authors_text":"Jan Goedgebeur, Jorik Jooken, Stijn Cambie, Tibo Van den Eede","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-11-26T07:56:46Z","title":"On the order-diameter ratio of girth-diameter cages"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.21144","kind":"arxiv","version":2},"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":"sha256:6a47fbd040d2f362faa00a55c7dd5489f99cb305cc2cba1c23a02b6e0f6fcb45","target":"record","created_at":"2026-06-29T01:14:26Z","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":"682beb96b92c322557e2cf9676f2f72ca2875048cc4bd7574aed470cde337a8f","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-11-26T07:56:46Z","title_canon_sha256":"d8b71ee27e660a1bab1eac61b6af46e06eef190d193f07bb8506fff774eb3883"},"schema_version":"1.0","source":{"id":"2511.21144","kind":"arxiv","version":2}},"canonical_sha256":"2e3e6acc81c038f4a116366bf36af23010dea3b4e235cba4b5bc5b5e1d6dc091","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e3e6acc81c038f4a116366bf36af23010dea3b4e235cba4b5bc5b5e1d6dc091","first_computed_at":"2026-06-29T01:14:26.703299Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-29T01:14:26.703299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ERGy8OSeJRzjh3u6pJFMzrDiWZdmitgtc88Z2x7lj5OVztkuVhjisVUJ7eSp8jKfjSMYW2ym9seMwaz9DOXABQ==","signature_status":"signed_v1","signed_at":"2026-06-29T01:14:26.703777Z","signed_message":"canonical_sha256_bytes"},"source_id":"2511.21144","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a47fbd040d2f362faa00a55c7dd5489f99cb305cc2cba1c23a02b6e0f6fcb45","sha256:5f95a48ab23b03c1bd0db5e75f66856bb724e6acc81bedd36a9c911e9b546c7c"],"state_sha256":"8b3d5f33cb3ebd0c3ec08c65a018466f64e1d616cbb8faa6042153a1681de039"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AzAlzLU+F+N51hQmIaJVavZUMdogkENLVlCu4mW4LbLAt3lxpvTzE8h3lO/LEPLuzJJwFu6zqUC89l5R+8IvCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T12:44:38.496040Z","bundle_sha256":"e3f931d54bddd3a3d0b08f4c0f81b42333686b3260e319f1217a191ae91c41bc"}}