{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:BZOX3NPSRDE5S2PSCUDGCYSAOR","short_pith_number":"pith:BZOX3NPS","canonical_record":{"source":{"id":"0905.2605","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2009-05-15T19:47:36Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"1a4f0d6b444721d85ce60f8256a32ba8c4993e8601d6ec8af5da01723195b20e","abstract_canon_sha256":"973aea7ac68bec376d218093196b72436af33e93523e76a8a1e8fafab4e9cd62"},"schema_version":"1.0"},"canonical_sha256":"0e5d7db5f288c9d969f21506616240746cb005f4838a10004ec327ae57ca32ad","source":{"kind":"arxiv","id":"0905.2605","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.2605","created_at":"2026-05-18T02:13:39Z"},{"alias_kind":"arxiv_version","alias_value":"0905.2605v2","created_at":"2026-05-18T02:13:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.2605","created_at":"2026-05-18T02:13:39Z"},{"alias_kind":"pith_short_12","alias_value":"BZOX3NPSRDE5","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BZOX3NPSRDE5S2PS","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BZOX3NPS","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:BZOX3NPSRDE5S2PSCUDGCYSAOR","target":"record","payload":{"canonical_record":{"source":{"id":"0905.2605","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2009-05-15T19:47:36Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"1a4f0d6b444721d85ce60f8256a32ba8c4993e8601d6ec8af5da01723195b20e","abstract_canon_sha256":"973aea7ac68bec376d218093196b72436af33e93523e76a8a1e8fafab4e9cd62"},"schema_version":"1.0"},"canonical_sha256":"0e5d7db5f288c9d969f21506616240746cb005f4838a10004ec327ae57ca32ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:13:39.166802Z","signature_b64":"dsEjSmYate0OAZDfzyclJfYoxgPXXHeu4NjuFkBObfJCKwSFIzr99PQpJkhQlm0ynsbnEr5JsADRj3+/hsEiDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e5d7db5f288c9d969f21506616240746cb005f4838a10004ec327ae57ca32ad","last_reissued_at":"2026-05-18T02:13:39.166453Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:13:39.166453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0905.2605","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":"2026-05-18T02:13:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eFH5gc5cmsnU8C3v67DD49OA4EEKyi4SpnIaRs7v76KsqKlFscetdThTA4/jM/626jDDFWrRiTnmDz7xN7zyDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:30:17.026840Z"},"content_sha256":"38af6593b8eaa892af018fecaca4447bca21a46c635f851d241d5d7d239a9672","schema_version":"1.0","event_id":"sha256:38af6593b8eaa892af018fecaca4447bca21a46c635f851d241d5d7d239a9672"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:BZOX3NPSRDE5S2PSCUDGCYSAOR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Emergence of Sparse Spanners and Greedy Well-Separated Pair Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Dengpan Zhou, Jie Gao","submitted_at":"2009-05-15T19:47:36Z","abstract_excerpt":"A spanner graph on a set of points in $R^d$ contains a shortest path between any pair of points with length at most a constant factor of their Euclidean distance. In this paper we investigate new models and aim to interpret why good spanners 'emerge' in reality, when they are clearly built in pieces by agents with their own interests and the construction is not coordinated. Our main result is to show that if edges are built in an arbitrary order but an edge is built if and only if its endpoints are not 'close' to the endpoints of an existing edge, the graph is a $(1 + \\eps)$-spanner with a lin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.2605","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":""},"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":"2026-05-18T02:13:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T7V8bKEI9bA/GIegCnXD6k7ifGdroL81yKopmZ3k9Gr9psu63oi8HTOtNRqmsZioJtpmu2nRErLT7SwFQ/W0Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:30:17.027222Z"},"content_sha256":"f705d63256ad120c1f80eade5033536c4f730c09dfbff3ca443cf6ef4d10a892","schema_version":"1.0","event_id":"sha256:f705d63256ad120c1f80eade5033536c4f730c09dfbff3ca443cf6ef4d10a892"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BZOX3NPSRDE5S2PSCUDGCYSAOR/bundle.json","state_url":"https://pith.science/pith/BZOX3NPSRDE5S2PSCUDGCYSAOR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BZOX3NPSRDE5S2PSCUDGCYSAOR/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":"2026-06-09T12:30:17Z","links":{"resolver":"https://pith.science/pith/BZOX3NPSRDE5S2PSCUDGCYSAOR","bundle":"https://pith.science/pith/BZOX3NPSRDE5S2PSCUDGCYSAOR/bundle.json","state":"https://pith.science/pith/BZOX3NPSRDE5S2PSCUDGCYSAOR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BZOX3NPSRDE5S2PSCUDGCYSAOR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:BZOX3NPSRDE5S2PSCUDGCYSAOR","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":"973aea7ac68bec376d218093196b72436af33e93523e76a8a1e8fafab4e9cd62","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2009-05-15T19:47:36Z","title_canon_sha256":"1a4f0d6b444721d85ce60f8256a32ba8c4993e8601d6ec8af5da01723195b20e"},"schema_version":"1.0","source":{"id":"0905.2605","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.2605","created_at":"2026-05-18T02:13:39Z"},{"alias_kind":"arxiv_version","alias_value":"0905.2605v2","created_at":"2026-05-18T02:13:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.2605","created_at":"2026-05-18T02:13:39Z"},{"alias_kind":"pith_short_12","alias_value":"BZOX3NPSRDE5","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BZOX3NPSRDE5S2PS","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BZOX3NPS","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:f705d63256ad120c1f80eade5033536c4f730c09dfbff3ca443cf6ef4d10a892","target":"graph","created_at":"2026-05-18T02:13:39Z","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":"A spanner graph on a set of points in $R^d$ contains a shortest path between any pair of points with length at most a constant factor of their Euclidean distance. In this paper we investigate new models and aim to interpret why good spanners 'emerge' in reality, when they are clearly built in pieces by agents with their own interests and the construction is not coordinated. Our main result is to show that if edges are built in an arbitrary order but an edge is built if and only if its endpoints are not 'close' to the endpoints of an existing edge, the graph is a $(1 + \\eps)$-spanner with a lin","authors_text":"Dengpan Zhou, Jie Gao","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2009-05-15T19:47:36Z","title":"The Emergence of Sparse Spanners and Greedy Well-Separated Pair Decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.2605","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":"sha256:38af6593b8eaa892af018fecaca4447bca21a46c635f851d241d5d7d239a9672","target":"record","created_at":"2026-05-18T02:13:39Z","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":"973aea7ac68bec376d218093196b72436af33e93523e76a8a1e8fafab4e9cd62","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2009-05-15T19:47:36Z","title_canon_sha256":"1a4f0d6b444721d85ce60f8256a32ba8c4993e8601d6ec8af5da01723195b20e"},"schema_version":"1.0","source":{"id":"0905.2605","kind":"arxiv","version":2}},"canonical_sha256":"0e5d7db5f288c9d969f21506616240746cb005f4838a10004ec327ae57ca32ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e5d7db5f288c9d969f21506616240746cb005f4838a10004ec327ae57ca32ad","first_computed_at":"2026-05-18T02:13:39.166453Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:13:39.166453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dsEjSmYate0OAZDfzyclJfYoxgPXXHeu4NjuFkBObfJCKwSFIzr99PQpJkhQlm0ynsbnEr5JsADRj3+/hsEiDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:13:39.166802Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.2605","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38af6593b8eaa892af018fecaca4447bca21a46c635f851d241d5d7d239a9672","sha256:f705d63256ad120c1f80eade5033536c4f730c09dfbff3ca443cf6ef4d10a892"],"state_sha256":"ec1e450700074df3a8bd26966fe237ddab9d5609ae4ba21a8d62dffa67d06a3c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5TVLuO47SeIp13+XoSMDbjb7jTwaxpd3d/JqSxn5VRdWZtNj0jx/uxLUg+xVwusIwPl1cOU4MOnfJRAxKit1DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T12:30:17.029098Z","bundle_sha256":"e21c3984eac40df529caca34a6d2fb6ee9abf6c784efb32326a97d42f98477ed"}}