{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ZS2HZHPYJVPT6FTWSSM24ZDNDB","short_pith_number":"pith:ZS2HZHPY","canonical_record":{"source":{"id":"1201.3123","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2012-01-15T21:02:50Z","cross_cats_sorted":["cs.DM","math-ph","math.MP","math.PR"],"title_canon_sha256":"8b53f5cf8e3ca3d12202a7c3705f73afce1292c7e3147bfe616c535e03a990fb","abstract_canon_sha256":"5fe28cf6aa307856b97a6cc9d34edcb7ce9cb13bc89eb27301b095aa4b96ecdb"},"schema_version":"1.0"},"canonical_sha256":"ccb47c9df84d5f3f16769499ae646d1867e320b8006f3ad955a94697c7ea175d","source":{"kind":"arxiv","id":"1201.3123","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3123","created_at":"2026-05-18T01:58:49Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3123v1","created_at":"2026-05-18T01:58:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3123","created_at":"2026-05-18T01:58:49Z"},{"alias_kind":"pith_short_12","alias_value":"ZS2HZHPYJVPT","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZS2HZHPYJVPT6FTW","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZS2HZHPY","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ZS2HZHPYJVPT6FTWSSM24ZDNDB","target":"record","payload":{"canonical_record":{"source":{"id":"1201.3123","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2012-01-15T21:02:50Z","cross_cats_sorted":["cs.DM","math-ph","math.MP","math.PR"],"title_canon_sha256":"8b53f5cf8e3ca3d12202a7c3705f73afce1292c7e3147bfe616c535e03a990fb","abstract_canon_sha256":"5fe28cf6aa307856b97a6cc9d34edcb7ce9cb13bc89eb27301b095aa4b96ecdb"},"schema_version":"1.0"},"canonical_sha256":"ccb47c9df84d5f3f16769499ae646d1867e320b8006f3ad955a94697c7ea175d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:58:49.073684Z","signature_b64":"8aSkDI65PJ4e5IuprnsV7TtJitG/7FlYtptg+RIZ3XYt5yvaYF4Lko3VJx5SymyVUluf0xhyB0t0Pqpo/zKUCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccb47c9df84d5f3f16769499ae646d1867e320b8006f3ad955a94697c7ea175d","last_reissued_at":"2026-05-18T01:58:49.072988Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:58:49.072988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.3123","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":"2026-05-18T01:58:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dFDZ4yrfoi9pvARk7Pxax57l3d3OH9/Ig2b4nnvw5SDpByNM5tWb++pL7etcVNYRKWDXCelIzh5ZzKuZaaPRDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:27:45.799809Z"},"content_sha256":"ec6dee3cce73bdbf8409cca7b127ada338f2146afbb118bedb7d3e0bb910be07","schema_version":"1.0","event_id":"sha256:ec6dee3cce73bdbf8409cca7b127ada338f2146afbb118bedb7d3e0bb910be07"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ZS2HZHPYJVPT6FTWSSM24ZDNDB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Full Connectivity: Corners, edges and faces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math-ph","math.MP","math.PR"],"primary_cat":"cond-mat.dis-nn","authors_text":"Carl P. Dettmann, Justin Coon, Orestis Georgiou","submitted_at":"2012-01-15T21:02:50Z","abstract_excerpt":"We develop a cluster expansion for the probability of full connectivity of high density random networks in confined geometries. In contrast to percolation phenomena at lower densities, boundary effects, which have previously been largely neglected, are not only relevant but dominant. We derive general analytical formulas that show a persistence of universality in a different form to percolation theory, and provide numerical confirmation. We also demonstrate the simplicity of our approach in three simple but instructive examples and discuss the practical benefits of its application to different"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3123","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":"2026-05-18T01:58:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Eefagt9vrmxwDtkJC2MObExj1X7MwqjzbSKbi0ce0MYgLP1+aNghijQPGfyTmRiNTomN/WPKbYXjNzw39LV0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:27:45.800472Z"},"content_sha256":"1d410bef7518e659fab20e0884cf14adc10fedabadc752d65801f36198d06803","schema_version":"1.0","event_id":"sha256:1d410bef7518e659fab20e0884cf14adc10fedabadc752d65801f36198d06803"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZS2HZHPYJVPT6FTWSSM24ZDNDB/bundle.json","state_url":"https://pith.science/pith/ZS2HZHPYJVPT6FTWSSM24ZDNDB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZS2HZHPYJVPT6FTWSSM24ZDNDB/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":"2026-05-28T15:27:45Z","links":{"resolver":"https://pith.science/pith/ZS2HZHPYJVPT6FTWSSM24ZDNDB","bundle":"https://pith.science/pith/ZS2HZHPYJVPT6FTWSSM24ZDNDB/bundle.json","state":"https://pith.science/pith/ZS2HZHPYJVPT6FTWSSM24ZDNDB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZS2HZHPYJVPT6FTWSSM24ZDNDB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZS2HZHPYJVPT6FTWSSM24ZDNDB","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":"5fe28cf6aa307856b97a6cc9d34edcb7ce9cb13bc89eb27301b095aa4b96ecdb","cross_cats_sorted":["cs.DM","math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2012-01-15T21:02:50Z","title_canon_sha256":"8b53f5cf8e3ca3d12202a7c3705f73afce1292c7e3147bfe616c535e03a990fb"},"schema_version":"1.0","source":{"id":"1201.3123","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3123","created_at":"2026-05-18T01:58:49Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3123v1","created_at":"2026-05-18T01:58:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3123","created_at":"2026-05-18T01:58:49Z"},{"alias_kind":"pith_short_12","alias_value":"ZS2HZHPYJVPT","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZS2HZHPYJVPT6FTW","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZS2HZHPY","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:1d410bef7518e659fab20e0884cf14adc10fedabadc752d65801f36198d06803","target":"graph","created_at":"2026-05-18T01:58:49Z","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 develop a cluster expansion for the probability of full connectivity of high density random networks in confined geometries. In contrast to percolation phenomena at lower densities, boundary effects, which have previously been largely neglected, are not only relevant but dominant. We derive general analytical formulas that show a persistence of universality in a different form to percolation theory, and provide numerical confirmation. We also demonstrate the simplicity of our approach in three simple but instructive examples and discuss the practical benefits of its application to different","authors_text":"Carl P. Dettmann, Justin Coon, Orestis Georgiou","cross_cats":["cs.DM","math-ph","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2012-01-15T21:02:50Z","title":"Full Connectivity: Corners, edges and faces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3123","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:ec6dee3cce73bdbf8409cca7b127ada338f2146afbb118bedb7d3e0bb910be07","target":"record","created_at":"2026-05-18T01:58:49Z","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":"5fe28cf6aa307856b97a6cc9d34edcb7ce9cb13bc89eb27301b095aa4b96ecdb","cross_cats_sorted":["cs.DM","math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2012-01-15T21:02:50Z","title_canon_sha256":"8b53f5cf8e3ca3d12202a7c3705f73afce1292c7e3147bfe616c535e03a990fb"},"schema_version":"1.0","source":{"id":"1201.3123","kind":"arxiv","version":1}},"canonical_sha256":"ccb47c9df84d5f3f16769499ae646d1867e320b8006f3ad955a94697c7ea175d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ccb47c9df84d5f3f16769499ae646d1867e320b8006f3ad955a94697c7ea175d","first_computed_at":"2026-05-18T01:58:49.072988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:49.072988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8aSkDI65PJ4e5IuprnsV7TtJitG/7FlYtptg+RIZ3XYt5yvaYF4Lko3VJx5SymyVUluf0xhyB0t0Pqpo/zKUCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:49.073684Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.3123","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec6dee3cce73bdbf8409cca7b127ada338f2146afbb118bedb7d3e0bb910be07","sha256:1d410bef7518e659fab20e0884cf14adc10fedabadc752d65801f36198d06803"],"state_sha256":"8766afb5fcd99e2a630eb1ff462574e24b49f302a095ee8ef21f69b9a44b7b6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"82MjjVYxHWfwwtMtds9UPfPw2b+gRLdioKbsU50HDn2/VXi4QU/AF9RJsFQ48izf4iUK3SvGfmThqyH2tYEgCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T15:27:45.803831Z","bundle_sha256":"0b0e7fb71d960b97d70f2ab8f39e20e211d31b107e45c988cc2e6490c12bc75f"}}