{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:UBO73Y2YBIVOSD2QRSAO2QHH2G","short_pith_number":"pith:UBO73Y2Y","canonical_record":{"source":{"id":"1204.4580","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-04-20T10:44:33Z","cross_cats_sorted":[],"title_canon_sha256":"50f0a2d7ce10ede7d297a042fba19a3b20553f91a92ee0843e5867cc7c8603ab","abstract_canon_sha256":"2ac235ae84689143b0c863adfbc6011bb26fe1a1235396cf0add0f75585c6f4a"},"schema_version":"1.0"},"canonical_sha256":"a05dfde3580a2ae90f508c80ed40e7d18fb5f669b32d2dde984a81b16339c5b4","source":{"kind":"arxiv","id":"1204.4580","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.4580","created_at":"2026-05-18T03:57:26Z"},{"alias_kind":"arxiv_version","alias_value":"1204.4580v1","created_at":"2026-05-18T03:57:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4580","created_at":"2026-05-18T03:57:26Z"},{"alias_kind":"pith_short_12","alias_value":"UBO73Y2YBIVO","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UBO73Y2YBIVOSD2Q","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UBO73Y2Y","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:UBO73Y2YBIVOSD2QRSAO2QHH2G","target":"record","payload":{"canonical_record":{"source":{"id":"1204.4580","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-04-20T10:44:33Z","cross_cats_sorted":[],"title_canon_sha256":"50f0a2d7ce10ede7d297a042fba19a3b20553f91a92ee0843e5867cc7c8603ab","abstract_canon_sha256":"2ac235ae84689143b0c863adfbc6011bb26fe1a1235396cf0add0f75585c6f4a"},"schema_version":"1.0"},"canonical_sha256":"a05dfde3580a2ae90f508c80ed40e7d18fb5f669b32d2dde984a81b16339c5b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:26.048586Z","signature_b64":"7Q6ne7T7ywnGQrxb47hGNuLaDsSK1Vj9NdWPTSmLylWEmW5Yf+q9lewGZ5Rx8I0c8+agjNdkBew0QNW1e36pCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a05dfde3580a2ae90f508c80ed40e7d18fb5f669b32d2dde984a81b16339c5b4","last_reissued_at":"2026-05-18T03:57:26.047816Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:26.047816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.4580","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":"2026-05-18T03:57:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CRFq1XcTJyO+eD/YeuNYoi6BHA7pXXtjHHWI9LUT3OqmP40H42O3JetOjpVYcxSgb8szpUW8EK2upwViid9GBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:19:03.353216Z"},"content_sha256":"b62ee9b9541f6c6a24a5cf7b7e02e69e178780786e5e2df8a44112f0132db1b7","schema_version":"1.0","event_id":"sha256:b62ee9b9541f6c6a24a5cf7b7e02e69e178780786e5e2df8a44112f0132db1b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:UBO73Y2YBIVOSD2QRSAO2QHH2G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The number of graphs of given diameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Younjin Kim, Zoltan Furedi","submitted_at":"2012-04-20T10:44:33Z","abstract_excerpt":"In this paper it is proved that there are constants 0< c_2< c_1 such that an asymptotic formula can be given for the the number of (labeled) n-vertex graphs of diameter d whenever n tends to infinity and 2 < d < n - c_1 (log n). A typical graph of diameter d consists of a combination of an induced path of length d and a highly connected block of size n-d+3. In the case d > n- c_2(log n) another asymptotic formula is calculated and the typical graph has a completely different snakelike structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4580","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":"2026-05-18T03:57:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wRsGNyBA2lZp7y6aAysmzqzZkkR7asLHDuFViQ8WVwk6/LXnS+6l0nsxgWVSSD6HfIT1FiWLRkAI6mq1aPgpDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:19:03.353859Z"},"content_sha256":"eb4ffe93d388e80fb63777b7bb1d8b9229eddc3a787cae3a0a388c2ffdd7e806","schema_version":"1.0","event_id":"sha256:eb4ffe93d388e80fb63777b7bb1d8b9229eddc3a787cae3a0a388c2ffdd7e806"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UBO73Y2YBIVOSD2QRSAO2QHH2G/bundle.json","state_url":"https://pith.science/pith/UBO73Y2YBIVOSD2QRSAO2QHH2G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UBO73Y2YBIVOSD2QRSAO2QHH2G/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":"2026-05-30T08:19:03Z","links":{"resolver":"https://pith.science/pith/UBO73Y2YBIVOSD2QRSAO2QHH2G","bundle":"https://pith.science/pith/UBO73Y2YBIVOSD2QRSAO2QHH2G/bundle.json","state":"https://pith.science/pith/UBO73Y2YBIVOSD2QRSAO2QHH2G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UBO73Y2YBIVOSD2QRSAO2QHH2G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UBO73Y2YBIVOSD2QRSAO2QHH2G","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":"2ac235ae84689143b0c863adfbc6011bb26fe1a1235396cf0add0f75585c6f4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-04-20T10:44:33Z","title_canon_sha256":"50f0a2d7ce10ede7d297a042fba19a3b20553f91a92ee0843e5867cc7c8603ab"},"schema_version":"1.0","source":{"id":"1204.4580","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.4580","created_at":"2026-05-18T03:57:26Z"},{"alias_kind":"arxiv_version","alias_value":"1204.4580v1","created_at":"2026-05-18T03:57:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4580","created_at":"2026-05-18T03:57:26Z"},{"alias_kind":"pith_short_12","alias_value":"UBO73Y2YBIVO","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UBO73Y2YBIVOSD2Q","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UBO73Y2Y","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:eb4ffe93d388e80fb63777b7bb1d8b9229eddc3a787cae3a0a388c2ffdd7e806","target":"graph","created_at":"2026-05-18T03:57:26Z","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"},"paper":{"abstract_excerpt":"In this paper it is proved that there are constants 0< c_2< c_1 such that an asymptotic formula can be given for the the number of (labeled) n-vertex graphs of diameter d whenever n tends to infinity and 2 < d < n - c_1 (log n). A typical graph of diameter d consists of a combination of an induced path of length d and a highly connected block of size n-d+3. In the case d > n- c_2(log n) another asymptotic formula is calculated and the typical graph has a completely different snakelike structure.","authors_text":"Younjin Kim, Zoltan Furedi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-04-20T10:44:33Z","title":"The number of graphs of given diameter"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4580","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:b62ee9b9541f6c6a24a5cf7b7e02e69e178780786e5e2df8a44112f0132db1b7","target":"record","created_at":"2026-05-18T03:57:26Z","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":"2ac235ae84689143b0c863adfbc6011bb26fe1a1235396cf0add0f75585c6f4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-04-20T10:44:33Z","title_canon_sha256":"50f0a2d7ce10ede7d297a042fba19a3b20553f91a92ee0843e5867cc7c8603ab"},"schema_version":"1.0","source":{"id":"1204.4580","kind":"arxiv","version":1}},"canonical_sha256":"a05dfde3580a2ae90f508c80ed40e7d18fb5f669b32d2dde984a81b16339c5b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a05dfde3580a2ae90f508c80ed40e7d18fb5f669b32d2dde984a81b16339c5b4","first_computed_at":"2026-05-18T03:57:26.047816Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:26.047816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Q6ne7T7ywnGQrxb47hGNuLaDsSK1Vj9NdWPTSmLylWEmW5Yf+q9lewGZ5Rx8I0c8+agjNdkBew0QNW1e36pCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:26.048586Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.4580","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b62ee9b9541f6c6a24a5cf7b7e02e69e178780786e5e2df8a44112f0132db1b7","sha256:eb4ffe93d388e80fb63777b7bb1d8b9229eddc3a787cae3a0a388c2ffdd7e806"],"state_sha256":"13931da9aba38c2364d66668e34fa017ea7610510aea96ee810bcbe5c3ea8a83"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a2NgnChMeXhcoWkTl6zOC9A3qeo8sAarP/DqpAHGrTqA9C5No1gg6jSf8gn61IT1lZXybQoSWCGC1DGOOsxFDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:19:03.357206Z","bundle_sha256":"75746ebde06bdadb7a1eba4208a7cadbb5143aee4372901d116274a6a50e718b"}}