{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:4EGCM64EFDJF7AXH5MF2HY45UI","short_pith_number":"pith:4EGCM64E","canonical_record":{"source":{"id":"1807.06220","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2018-07-17T04:43:01Z","cross_cats_sorted":[],"title_canon_sha256":"89e26c9f848d36440f84be3090fb23422899b2efd6ad9ba0c7ae439697db9ceb","abstract_canon_sha256":"8ef2b63f6720ba322640db7565300b3cf5a724ec21e0eed8b29019c7be64b512"},"schema_version":"1.0"},"canonical_sha256":"e10c267b8428d25f82e7eb0ba3e39da23e0f391927d71ae987f5d1f065b9f611","source":{"kind":"arxiv","id":"1807.06220","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.06220","created_at":"2026-05-18T00:04:14Z"},{"alias_kind":"arxiv_version","alias_value":"1807.06220v2","created_at":"2026-05-18T00:04:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.06220","created_at":"2026-05-18T00:04:14Z"},{"alias_kind":"pith_short_12","alias_value":"4EGCM64EFDJF","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4EGCM64EFDJF7AXH","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4EGCM64E","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:4EGCM64EFDJF7AXH5MF2HY45UI","target":"record","payload":{"canonical_record":{"source":{"id":"1807.06220","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2018-07-17T04:43:01Z","cross_cats_sorted":[],"title_canon_sha256":"89e26c9f848d36440f84be3090fb23422899b2efd6ad9ba0c7ae439697db9ceb","abstract_canon_sha256":"8ef2b63f6720ba322640db7565300b3cf5a724ec21e0eed8b29019c7be64b512"},"schema_version":"1.0"},"canonical_sha256":"e10c267b8428d25f82e7eb0ba3e39da23e0f391927d71ae987f5d1f065b9f611","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:14.376698Z","signature_b64":"oC8wiyMyrKHp5DgdHj4esyPCMpoJpcqRJNtD5dLCs+wvOJsnrGavDAOnZfRrJtEFFGH7yePWXoj6B9IB6IpBAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e10c267b8428d25f82e7eb0ba3e39da23e0f391927d71ae987f5d1f065b9f611","last_reissued_at":"2026-05-18T00:04:14.375877Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:14.375877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.06220","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":"2026-05-18T00:04:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WOFIRZLqC6B7GehJLKWk4u7ICTwDlDhs4CthL7Y70uFDqcHo/3ZncXGgiPdOx9OgKqgznQPpNxwMffvjpTFxCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T19:55:12.728764Z"},"content_sha256":"8f7da9e1a883712f87f350bfd7897b191a40bcc53f79b82cad5f31f05264f057","schema_version":"1.0","event_id":"sha256:8f7da9e1a883712f87f350bfd7897b191a40bcc53f79b82cad5f31f05264f057"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:4EGCM64EFDJF7AXH5MF2HY45UI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random spherical graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.soc-ph","authors_text":"Alfonso Allen-Perkins","submitted_at":"2018-07-17T04:43:01Z","abstract_excerpt":"This work addresses a modification of the random geometric graph (RGG) model by considering a set of points uniformly and independently distributed on the surface of a $(d-1)$-sphere with radius $r$ in a $d-$dimensional Euclidean space, instead of on an unit hypercube $[0,1]^d$ . Then, two vertices are connected by a link if their great circle distance is at most $s$. In the case of $d=3$, the topological properties of the random spherical graphs (RSGs) generated by this model are studied as a function of $s$. We obtain analytical expressions for the average degree, degree distribution, connec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06220","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":"2026-05-18T00:04:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sOnvNYOxIgxbcSe/vhcDgmqbg3tnRrh+vGXLQYQrcpbG92rMW9I+2IWPiqM6jWe3w1u74obr7uDesjG8HVBJCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T19:55:12.729103Z"},"content_sha256":"3790bf28218e482168f3497ff90a14c67fcf34255f798fa2061e272e54b52406","schema_version":"1.0","event_id":"sha256:3790bf28218e482168f3497ff90a14c67fcf34255f798fa2061e272e54b52406"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4EGCM64EFDJF7AXH5MF2HY45UI/bundle.json","state_url":"https://pith.science/pith/4EGCM64EFDJF7AXH5MF2HY45UI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4EGCM64EFDJF7AXH5MF2HY45UI/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":"2026-07-01T19:55:12Z","links":{"resolver":"https://pith.science/pith/4EGCM64EFDJF7AXH5MF2HY45UI","bundle":"https://pith.science/pith/4EGCM64EFDJF7AXH5MF2HY45UI/bundle.json","state":"https://pith.science/pith/4EGCM64EFDJF7AXH5MF2HY45UI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4EGCM64EFDJF7AXH5MF2HY45UI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4EGCM64EFDJF7AXH5MF2HY45UI","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":"8ef2b63f6720ba322640db7565300b3cf5a724ec21e0eed8b29019c7be64b512","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2018-07-17T04:43:01Z","title_canon_sha256":"89e26c9f848d36440f84be3090fb23422899b2efd6ad9ba0c7ae439697db9ceb"},"schema_version":"1.0","source":{"id":"1807.06220","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.06220","created_at":"2026-05-18T00:04:14Z"},{"alias_kind":"arxiv_version","alias_value":"1807.06220v2","created_at":"2026-05-18T00:04:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.06220","created_at":"2026-05-18T00:04:14Z"},{"alias_kind":"pith_short_12","alias_value":"4EGCM64EFDJF","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4EGCM64EFDJF7AXH","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4EGCM64E","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:3790bf28218e482168f3497ff90a14c67fcf34255f798fa2061e272e54b52406","target":"graph","created_at":"2026-05-18T00:04:14Z","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":"This work addresses a modification of the random geometric graph (RGG) model by considering a set of points uniformly and independently distributed on the surface of a $(d-1)$-sphere with radius $r$ in a $d-$dimensional Euclidean space, instead of on an unit hypercube $[0,1]^d$ . Then, two vertices are connected by a link if their great circle distance is at most $s$. In the case of $d=3$, the topological properties of the random spherical graphs (RSGs) generated by this model are studied as a function of $s$. We obtain analytical expressions for the average degree, degree distribution, connec","authors_text":"Alfonso Allen-Perkins","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2018-07-17T04:43:01Z","title":"Random spherical graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06220","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":"sha256:8f7da9e1a883712f87f350bfd7897b191a40bcc53f79b82cad5f31f05264f057","target":"record","created_at":"2026-05-18T00:04:14Z","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":"8ef2b63f6720ba322640db7565300b3cf5a724ec21e0eed8b29019c7be64b512","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2018-07-17T04:43:01Z","title_canon_sha256":"89e26c9f848d36440f84be3090fb23422899b2efd6ad9ba0c7ae439697db9ceb"},"schema_version":"1.0","source":{"id":"1807.06220","kind":"arxiv","version":2}},"canonical_sha256":"e10c267b8428d25f82e7eb0ba3e39da23e0f391927d71ae987f5d1f065b9f611","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e10c267b8428d25f82e7eb0ba3e39da23e0f391927d71ae987f5d1f065b9f611","first_computed_at":"2026-05-18T00:04:14.375877Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:14.375877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oC8wiyMyrKHp5DgdHj4esyPCMpoJpcqRJNtD5dLCs+wvOJsnrGavDAOnZfRrJtEFFGH7yePWXoj6B9IB6IpBAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:14.376698Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.06220","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f7da9e1a883712f87f350bfd7897b191a40bcc53f79b82cad5f31f05264f057","sha256:3790bf28218e482168f3497ff90a14c67fcf34255f798fa2061e272e54b52406"],"state_sha256":"4e9e31e8fbc2f1b3a049b19041347a691b4cde686285e2b0bfcf33b3575b1891"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6mi8Neh6qnEgNimfdLOvbcN2W0TIpkyeVB3BjUf67sCzabqcECoatpOB9OwMjJs5+mKuZUJFlac3SXT7bmWBAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T19:55:12.730992Z","bundle_sha256":"b2388b310b2736e059a7adc8b521fc824a7507c6dd21e87669895df3409035c9"}}