{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:4H4EDRRIKUD6EVDD2JPI5WN276","short_pith_number":"pith:4H4EDRRI","canonical_record":{"source":{"id":"1401.0115","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-31T09:11:11Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"29a4ba37945ac6dfcf7076f53adf57a3d78540dbbfe51a6fce81c9b20f569ebc","abstract_canon_sha256":"4739930cd379bc1632937ad72da2e3c9714510958b353b1c20462fdf7929c0ce"},"schema_version":"1.0"},"canonical_sha256":"e1f841c6285507e25463d25e8ed9baff8e927bf282d6d9edf95ec3cb1b11b688","source":{"kind":"arxiv","id":"1401.0115","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0115","created_at":"2026-05-18T02:46:22Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0115v2","created_at":"2026-05-18T02:46:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0115","created_at":"2026-05-18T02:46:22Z"},{"alias_kind":"pith_short_12","alias_value":"4H4EDRRIKUD6","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4H4EDRRIKUD6EVDD","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4H4EDRRI","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:4H4EDRRIKUD6EVDD2JPI5WN276","target":"record","payload":{"canonical_record":{"source":{"id":"1401.0115","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-31T09:11:11Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"29a4ba37945ac6dfcf7076f53adf57a3d78540dbbfe51a6fce81c9b20f569ebc","abstract_canon_sha256":"4739930cd379bc1632937ad72da2e3c9714510958b353b1c20462fdf7929c0ce"},"schema_version":"1.0"},"canonical_sha256":"e1f841c6285507e25463d25e8ed9baff8e927bf282d6d9edf95ec3cb1b11b688","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:22.664868Z","signature_b64":"VwRIigSR4DrwH4/7v2u1uMmmtrGgUQ/U4w7OdbsFnxgfuvHOEs5HEa7FDEy3GMhSKhs5nYAQBvUcHmyEtpgmBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1f841c6285507e25463d25e8ed9baff8e927bf282d6d9edf95ec3cb1b11b688","last_reissued_at":"2026-05-18T02:46:22.664417Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:22.664417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.0115","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":"2026-05-18T02:46:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1LY4JlcpsMaLfYJ0Q+BuiOPJaXXRfex+WecZjjKKG60lGzzYPsjjfnp701+BRUNVEIBTJuYSdLXXHdQ3wJbZCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:22:40.315399Z"},"content_sha256":"943ceaaad9216a60265c66243c9ed102c6ecdae90860266913c26612aeb20eb8","schema_version":"1.0","event_id":"sha256:943ceaaad9216a60265c66243c9ed102c6ecdae90860266913c26612aeb20eb8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:4H4EDRRIKUD6EVDD2JPI5WN276","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Opinion Dynamics and Influencing on Random Geometric Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"math.DS","authors_text":"B. K. Szymanski, Chjan Lim, G. Korniss, Weituo Zhang","submitted_at":"2013-12-31T09:11:11Z","abstract_excerpt":"We investigate the two-word Naming Game on two-dimensional random geometric graphs. Studying this model advances our understanding of the spatial distribution and propagation of opinions in social dynamics. A main feature of this model is the spontaneous emergence of spatial structures called opinion domains which are geographic regions with clear boundaries within which all individuals share the same opinion. We provide the mean-field equation for the underlying dynamics and discuss several properties of the equation such as the stationary solutions and two-time-scale separation. For the evol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0115","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":"2026-05-18T02:46:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PVUrMxDACXXr8fTRj974oVuUp+FDQDDgCWskDlwnYKbwArzSwNMo3r1QDmiM+1hjlFXXUZNnNtass2k/qqluBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:22:40.316089Z"},"content_sha256":"a1472cf807e5d964f465ae12d185e2a41a161faaef5129ee3e23c87295cfde2f","schema_version":"1.0","event_id":"sha256:a1472cf807e5d964f465ae12d185e2a41a161faaef5129ee3e23c87295cfde2f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4H4EDRRIKUD6EVDD2JPI5WN276/bundle.json","state_url":"https://pith.science/pith/4H4EDRRIKUD6EVDD2JPI5WN276/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4H4EDRRIKUD6EVDD2JPI5WN276/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":"2026-05-25T12:22:40Z","links":{"resolver":"https://pith.science/pith/4H4EDRRIKUD6EVDD2JPI5WN276","bundle":"https://pith.science/pith/4H4EDRRIKUD6EVDD2JPI5WN276/bundle.json","state":"https://pith.science/pith/4H4EDRRIKUD6EVDD2JPI5WN276/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4H4EDRRIKUD6EVDD2JPI5WN276/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4H4EDRRIKUD6EVDD2JPI5WN276","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":"4739930cd379bc1632937ad72da2e3c9714510958b353b1c20462fdf7929c0ce","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-31T09:11:11Z","title_canon_sha256":"29a4ba37945ac6dfcf7076f53adf57a3d78540dbbfe51a6fce81c9b20f569ebc"},"schema_version":"1.0","source":{"id":"1401.0115","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0115","created_at":"2026-05-18T02:46:22Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0115v2","created_at":"2026-05-18T02:46:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0115","created_at":"2026-05-18T02:46:22Z"},{"alias_kind":"pith_short_12","alias_value":"4H4EDRRIKUD6","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4H4EDRRIKUD6EVDD","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4H4EDRRI","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:a1472cf807e5d964f465ae12d185e2a41a161faaef5129ee3e23c87295cfde2f","target":"graph","created_at":"2026-05-18T02:46:22Z","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 investigate the two-word Naming Game on two-dimensional random geometric graphs. Studying this model advances our understanding of the spatial distribution and propagation of opinions in social dynamics. A main feature of this model is the spontaneous emergence of spatial structures called opinion domains which are geographic regions with clear boundaries within which all individuals share the same opinion. We provide the mean-field equation for the underlying dynamics and discuss several properties of the equation such as the stationary solutions and two-time-scale separation. For the evol","authors_text":"B. K. Szymanski, Chjan Lim, G. Korniss, Weituo Zhang","cross_cats":["physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-31T09:11:11Z","title":"Opinion Dynamics and Influencing on Random Geometric Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0115","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":"sha256:943ceaaad9216a60265c66243c9ed102c6ecdae90860266913c26612aeb20eb8","target":"record","created_at":"2026-05-18T02:46:22Z","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":"4739930cd379bc1632937ad72da2e3c9714510958b353b1c20462fdf7929c0ce","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-31T09:11:11Z","title_canon_sha256":"29a4ba37945ac6dfcf7076f53adf57a3d78540dbbfe51a6fce81c9b20f569ebc"},"schema_version":"1.0","source":{"id":"1401.0115","kind":"arxiv","version":2}},"canonical_sha256":"e1f841c6285507e25463d25e8ed9baff8e927bf282d6d9edf95ec3cb1b11b688","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1f841c6285507e25463d25e8ed9baff8e927bf282d6d9edf95ec3cb1b11b688","first_computed_at":"2026-05-18T02:46:22.664417Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:22.664417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VwRIigSR4DrwH4/7v2u1uMmmtrGgUQ/U4w7OdbsFnxgfuvHOEs5HEa7FDEy3GMhSKhs5nYAQBvUcHmyEtpgmBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:22.664868Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0115","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:943ceaaad9216a60265c66243c9ed102c6ecdae90860266913c26612aeb20eb8","sha256:a1472cf807e5d964f465ae12d185e2a41a161faaef5129ee3e23c87295cfde2f"],"state_sha256":"53f9a432c62f9342659509a2eb4b4ed6268c48d715ea8c601b54f21ceff94d6b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8cExsQR9OrRbuUKNrDeO59Gp2YIEURhDrfswXey1xdsbrd3fbl+I0rC7X2qDRa5FFgGsVjNI/L1VlmOuO9tdCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T12:22:40.319881Z","bundle_sha256":"f83eefe178eea430534c5b1bc96182eb7aa0e15ac5b2c10133358e56863ba0ff"}}