{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:JNYDL4GYZSLKVP44VIAGPFRFHB","short_pith_number":"pith:JNYDL4GY","canonical_record":{"source":{"id":"1409.5366","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2014-09-18T16:33:45Z","cross_cats_sorted":[],"title_canon_sha256":"9781bc4eb3cd67d35f28f4f9c29ab24fbb50a4f43276eee74f1b9f7cbde78c62","abstract_canon_sha256":"0da311da5bf837309840ea6e3153ad47aeb922b113b8bf2e907a600295641817"},"schema_version":"1.0"},"canonical_sha256":"4b7035f0d8cc96aabf9caa006796253864a3fc69337a5f11ec4f8de4099df914","source":{"kind":"arxiv","id":"1409.5366","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5366","created_at":"2026-05-18T02:42:29Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5366v1","created_at":"2026-05-18T02:42:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5366","created_at":"2026-05-18T02:42:29Z"},{"alias_kind":"pith_short_12","alias_value":"JNYDL4GYZSLK","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JNYDL4GYZSLKVP44","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JNYDL4GY","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:JNYDL4GYZSLKVP44VIAGPFRFHB","target":"record","payload":{"canonical_record":{"source":{"id":"1409.5366","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2014-09-18T16:33:45Z","cross_cats_sorted":[],"title_canon_sha256":"9781bc4eb3cd67d35f28f4f9c29ab24fbb50a4f43276eee74f1b9f7cbde78c62","abstract_canon_sha256":"0da311da5bf837309840ea6e3153ad47aeb922b113b8bf2e907a600295641817"},"schema_version":"1.0"},"canonical_sha256":"4b7035f0d8cc96aabf9caa006796253864a3fc69337a5f11ec4f8de4099df914","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:29.715338Z","signature_b64":"S9l0AtFaYRIEp41DW/cL28a9o83ZkIxisoY7uC2+BfoNbtw+Klylu4StCMb+a/RdLEaSXxsJphhLaXAOrGOJBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b7035f0d8cc96aabf9caa006796253864a3fc69337a5f11ec4f8de4099df914","last_reissued_at":"2026-05-18T02:42:29.714509Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:29.714509Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.5366","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":"2026-05-18T02:42:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kpuc8URPEy5EANNaqTdBn4UkXTsvFU9CdlIwtde3AZtUIgkAGc4zCe03Zf0f33xVATlQxxgon/dgD03nhTAXBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:17:25.690697Z"},"content_sha256":"e656e025b0de2e4f975acd52250673a63f257d5b27c1ff3ece7d92fa0cfdbfe9","schema_version":"1.0","event_id":"sha256:e656e025b0de2e4f975acd52250673a63f257d5b27c1ff3ece7d92fa0cfdbfe9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:JNYDL4GYZSLKVP44VIAGPFRFHB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quality of Service in Network Creation Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Alexander M\\\"acker, Andreas Cord-Landwehr, Friedhelm Meyer auf der Heide","submitted_at":"2014-09-18T16:33:45Z","abstract_excerpt":"Network creation games model the creation and usage costs of networks formed by n selfish nodes. Each node v can buy a set of edges, each for a fixed price \\alpha > 0. Its goal is to minimize its private costs, i.e., the sum (SUM-game, Fabrikant et al., PODC 2003) or maximum (MAX-game, Demaine et al., PODC 2007) of distances from $v$ to all other nodes plus the prices of the bought edges. The above papers show the existence of Nash equilibria as well as upper and lower bounds for the prices of anarchy and stability. In several subsequent papers, these bounds were improved for a wide range of p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5366","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":"2026-05-18T02:42:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w2N3CF8owlMJnlub+duatIOkWBgv24qadDSVfrFnyDVFghJnQllhXQWU+rdqum6eAkjPeMM3np93eBX+65iXAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:17:25.691205Z"},"content_sha256":"87daa7d913402812b4cd4ea25d40bf8d5d73fbcb8be494b0708142fd889a0a4c","schema_version":"1.0","event_id":"sha256:87daa7d913402812b4cd4ea25d40bf8d5d73fbcb8be494b0708142fd889a0a4c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JNYDL4GYZSLKVP44VIAGPFRFHB/bundle.json","state_url":"https://pith.science/pith/JNYDL4GYZSLKVP44VIAGPFRFHB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JNYDL4GYZSLKVP44VIAGPFRFHB/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":"2026-06-01T05:17:25Z","links":{"resolver":"https://pith.science/pith/JNYDL4GYZSLKVP44VIAGPFRFHB","bundle":"https://pith.science/pith/JNYDL4GYZSLKVP44VIAGPFRFHB/bundle.json","state":"https://pith.science/pith/JNYDL4GYZSLKVP44VIAGPFRFHB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JNYDL4GYZSLKVP44VIAGPFRFHB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JNYDL4GYZSLKVP44VIAGPFRFHB","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":"0da311da5bf837309840ea6e3153ad47aeb922b113b8bf2e907a600295641817","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2014-09-18T16:33:45Z","title_canon_sha256":"9781bc4eb3cd67d35f28f4f9c29ab24fbb50a4f43276eee74f1b9f7cbde78c62"},"schema_version":"1.0","source":{"id":"1409.5366","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5366","created_at":"2026-05-18T02:42:29Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5366v1","created_at":"2026-05-18T02:42:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5366","created_at":"2026-05-18T02:42:29Z"},{"alias_kind":"pith_short_12","alias_value":"JNYDL4GYZSLK","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JNYDL4GYZSLKVP44","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JNYDL4GY","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:87daa7d913402812b4cd4ea25d40bf8d5d73fbcb8be494b0708142fd889a0a4c","target":"graph","created_at":"2026-05-18T02:42:29Z","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":"Network creation games model the creation and usage costs of networks formed by n selfish nodes. Each node v can buy a set of edges, each for a fixed price \\alpha > 0. Its goal is to minimize its private costs, i.e., the sum (SUM-game, Fabrikant et al., PODC 2003) or maximum (MAX-game, Demaine et al., PODC 2007) of distances from $v$ to all other nodes plus the prices of the bought edges. The above papers show the existence of Nash equilibria as well as upper and lower bounds for the prices of anarchy and stability. In several subsequent papers, these bounds were improved for a wide range of p","authors_text":"Alexander M\\\"acker, Andreas Cord-Landwehr, Friedhelm Meyer auf der Heide","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2014-09-18T16:33:45Z","title":"Quality of Service in Network Creation Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5366","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:e656e025b0de2e4f975acd52250673a63f257d5b27c1ff3ece7d92fa0cfdbfe9","target":"record","created_at":"2026-05-18T02:42:29Z","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":"0da311da5bf837309840ea6e3153ad47aeb922b113b8bf2e907a600295641817","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2014-09-18T16:33:45Z","title_canon_sha256":"9781bc4eb3cd67d35f28f4f9c29ab24fbb50a4f43276eee74f1b9f7cbde78c62"},"schema_version":"1.0","source":{"id":"1409.5366","kind":"arxiv","version":1}},"canonical_sha256":"4b7035f0d8cc96aabf9caa006796253864a3fc69337a5f11ec4f8de4099df914","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b7035f0d8cc96aabf9caa006796253864a3fc69337a5f11ec4f8de4099df914","first_computed_at":"2026-05-18T02:42:29.714509Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:29.714509Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S9l0AtFaYRIEp41DW/cL28a9o83ZkIxisoY7uC2+BfoNbtw+Klylu4StCMb+a/RdLEaSXxsJphhLaXAOrGOJBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:29.715338Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.5366","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e656e025b0de2e4f975acd52250673a63f257d5b27c1ff3ece7d92fa0cfdbfe9","sha256:87daa7d913402812b4cd4ea25d40bf8d5d73fbcb8be494b0708142fd889a0a4c"],"state_sha256":"6b8072003b12a8eed3bf1909af94144329c232a7b816be7ff3efe392924d0499"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zB4C5Baw/vdKmFZRjD1G/VblzCgUxnkE525zWBwHQ6Mj1wMoUJGI5pOns4sCP4cd6vagX+P2mpY2IiJzsyVKCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T05:17:25.694065Z","bundle_sha256":"a84f26e50cfe33dfc3c0b34b81d862d0bdfe3a21d9d918b5e758e430d34de21d"}}