{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:TMVPZOCOV7WPHK6YLS2VTBKCDC","short_pith_number":"pith:TMVPZOCO","canonical_record":{"source":{"id":"1704.06400","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-21T05:01:10Z","cross_cats_sorted":[],"title_canon_sha256":"12a1b32b75789f83a1abcb27b655fc1559a198fecc4c2c9610dece609736fab2","abstract_canon_sha256":"a1781bcb46e337fc7afe4df4a39a772664e518a2a113f0f27a78e192bed154b8"},"schema_version":"1.0"},"canonical_sha256":"9b2afcb84eafecf3abd85cb5598542188e0b0f71759a73d0f35cbd1f0cf4759d","source":{"kind":"arxiv","id":"1704.06400","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06400","created_at":"2026-05-18T00:24:10Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06400v3","created_at":"2026-05-18T00:24:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06400","created_at":"2026-05-18T00:24:10Z"},{"alias_kind":"pith_short_12","alias_value":"TMVPZOCOV7WP","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TMVPZOCOV7WPHK6Y","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TMVPZOCO","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:TMVPZOCOV7WPHK6YLS2VTBKCDC","target":"record","payload":{"canonical_record":{"source":{"id":"1704.06400","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-21T05:01:10Z","cross_cats_sorted":[],"title_canon_sha256":"12a1b32b75789f83a1abcb27b655fc1559a198fecc4c2c9610dece609736fab2","abstract_canon_sha256":"a1781bcb46e337fc7afe4df4a39a772664e518a2a113f0f27a78e192bed154b8"},"schema_version":"1.0"},"canonical_sha256":"9b2afcb84eafecf3abd85cb5598542188e0b0f71759a73d0f35cbd1f0cf4759d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:10.272004Z","signature_b64":"tVX+c119en4JTa4wRONYvQHMI2Xv16UYYRAD0H53jCXeu83PpZpOWUX3Z4f0bvvRabLcTciiDDqH1XW+ygnlCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b2afcb84eafecf3abd85cb5598542188e0b0f71759a73d0f35cbd1f0cf4759d","last_reissued_at":"2026-05-18T00:24:10.271371Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:10.271371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.06400","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:24:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vGgY4NwJ3yaOQ2xBZ5eVDqkxw9j6RBt8QhU2ERbyBi19ttkKBCu5cdh1WJMGtGTtDb7bXFKAxm+C+uGcJY0EBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:18:41.381748Z"},"content_sha256":"6b0e255d1dab9ccd921bbf0f2397088254568d42d8f6a69e0e864e2555d1fe92","schema_version":"1.0","event_id":"sha256:6b0e255d1dab9ccd921bbf0f2397088254568d42d8f6a69e0e864e2555d1fe92"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:TMVPZOCOV7WPHK6YLS2VTBKCDC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counting k-Hop Paths in the Random Connection Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander P. Kartun-Giles, Sunwoo Kim","submitted_at":"2017-04-21T05:01:10Z","abstract_excerpt":"We study, via combinatorial enumeration, the probability of k-hop connection between two nodes in a wireless multi-hop network. This addresses the difficulty of providing an exact formula for the scaling of hop counts with Euclidean distance without first making a sort of mean field approximation, which in this case assumes all nodes in the network have uncorrelated degrees. We therefore study the mean and variance of the number of k-hop paths between two vertices x,y in the random connection model, which is a random geometric graph where nodes connect probabilistically rather than determinist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06400","kind":"arxiv","version":3},"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":"2026-05-18T00:24:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j6u5apEvZFr0qozMVHaP4LUiYmiWlGOBGmTi5C32HhikpHo03N40uNYctZJJtrJXGLCnOfxn3/pJwdcjtPIMCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:18:41.382096Z"},"content_sha256":"1a880a6a90319552f108e7d1cc66f750ec677b33cabfb890a6f7cb02c86b1088","schema_version":"1.0","event_id":"sha256:1a880a6a90319552f108e7d1cc66f750ec677b33cabfb890a6f7cb02c86b1088"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TMVPZOCOV7WPHK6YLS2VTBKCDC/bundle.json","state_url":"https://pith.science/pith/TMVPZOCOV7WPHK6YLS2VTBKCDC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TMVPZOCOV7WPHK6YLS2VTBKCDC/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":"2026-06-24T07:18:41Z","links":{"resolver":"https://pith.science/pith/TMVPZOCOV7WPHK6YLS2VTBKCDC","bundle":"https://pith.science/pith/TMVPZOCOV7WPHK6YLS2VTBKCDC/bundle.json","state":"https://pith.science/pith/TMVPZOCOV7WPHK6YLS2VTBKCDC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TMVPZOCOV7WPHK6YLS2VTBKCDC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TMVPZOCOV7WPHK6YLS2VTBKCDC","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":"a1781bcb46e337fc7afe4df4a39a772664e518a2a113f0f27a78e192bed154b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-21T05:01:10Z","title_canon_sha256":"12a1b32b75789f83a1abcb27b655fc1559a198fecc4c2c9610dece609736fab2"},"schema_version":"1.0","source":{"id":"1704.06400","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06400","created_at":"2026-05-18T00:24:10Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06400v3","created_at":"2026-05-18T00:24:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06400","created_at":"2026-05-18T00:24:10Z"},{"alias_kind":"pith_short_12","alias_value":"TMVPZOCOV7WP","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TMVPZOCOV7WPHK6Y","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TMVPZOCO","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:1a880a6a90319552f108e7d1cc66f750ec677b33cabfb890a6f7cb02c86b1088","target":"graph","created_at":"2026-05-18T00:24:10Z","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 study, via combinatorial enumeration, the probability of k-hop connection between two nodes in a wireless multi-hop network. This addresses the difficulty of providing an exact formula for the scaling of hop counts with Euclidean distance without first making a sort of mean field approximation, which in this case assumes all nodes in the network have uncorrelated degrees. We therefore study the mean and variance of the number of k-hop paths between two vertices x,y in the random connection model, which is a random geometric graph where nodes connect probabilistically rather than determinist","authors_text":"Alexander P. Kartun-Giles, Sunwoo Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-21T05:01:10Z","title":"Counting k-Hop Paths in the Random Connection Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06400","kind":"arxiv","version":3},"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":"sha256:6b0e255d1dab9ccd921bbf0f2397088254568d42d8f6a69e0e864e2555d1fe92","target":"record","created_at":"2026-05-18T00:24:10Z","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":"a1781bcb46e337fc7afe4df4a39a772664e518a2a113f0f27a78e192bed154b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-21T05:01:10Z","title_canon_sha256":"12a1b32b75789f83a1abcb27b655fc1559a198fecc4c2c9610dece609736fab2"},"schema_version":"1.0","source":{"id":"1704.06400","kind":"arxiv","version":3}},"canonical_sha256":"9b2afcb84eafecf3abd85cb5598542188e0b0f71759a73d0f35cbd1f0cf4759d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b2afcb84eafecf3abd85cb5598542188e0b0f71759a73d0f35cbd1f0cf4759d","first_computed_at":"2026-05-18T00:24:10.271371Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:10.271371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tVX+c119en4JTa4wRONYvQHMI2Xv16UYYRAD0H53jCXeu83PpZpOWUX3Z4f0bvvRabLcTciiDDqH1XW+ygnlCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:10.272004Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.06400","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b0e255d1dab9ccd921bbf0f2397088254568d42d8f6a69e0e864e2555d1fe92","sha256:1a880a6a90319552f108e7d1cc66f750ec677b33cabfb890a6f7cb02c86b1088"],"state_sha256":"681a0376e4053e3db976d34ee9962eaae65de36daa0fa131d3e8f48fa5dcc5a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ih7mgbtH2qxmONBpa6ecB/lZF+akCZwgkxoPrpkGoSafi8HRd+8sV5feJtM+QjQAQUfyCYWYOa7LxrJeO8DhCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T07:18:41.384067Z","bundle_sha256":"ce6647c04c16ec880687c2abbce551794322b1b75669cb9a6a0905b41c10d7a2"}}