{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:AF4EP3VYLBGWEQNNCP5XUDQ7CU","short_pith_number":"pith:AF4EP3VY","canonical_record":{"source":{"id":"1305.3688","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2013-05-16T06:17:51Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"71bb65906c38ccee776ba52314650ce33b53a4f26ff15c96403f97f0a98b8f44","abstract_canon_sha256":"6b1c641722323391b580a6fd30fee52ffc8831ce978ec7a45263938f1e870cb7"},"schema_version":"1.0"},"canonical_sha256":"017847eeb8584d6241ad13fb7a0e1f153ada45b6a1e297d1b2f8ced2478fc2eb","source":{"kind":"arxiv","id":"1305.3688","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.3688","created_at":"2026-05-18T03:16:38Z"},{"alias_kind":"arxiv_version","alias_value":"1305.3688v2","created_at":"2026-05-18T03:16:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3688","created_at":"2026-05-18T03:16:38Z"},{"alias_kind":"pith_short_12","alias_value":"AF4EP3VYLBGW","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AF4EP3VYLBGWEQNN","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AF4EP3VY","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:AF4EP3VYLBGWEQNNCP5XUDQ7CU","target":"record","payload":{"canonical_record":{"source":{"id":"1305.3688","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2013-05-16T06:17:51Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"71bb65906c38ccee776ba52314650ce33b53a4f26ff15c96403f97f0a98b8f44","abstract_canon_sha256":"6b1c641722323391b580a6fd30fee52ffc8831ce978ec7a45263938f1e870cb7"},"schema_version":"1.0"},"canonical_sha256":"017847eeb8584d6241ad13fb7a0e1f153ada45b6a1e297d1b2f8ced2478fc2eb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:38.275541Z","signature_b64":"XMlpVfKEWjVtJQ6i1ZvaDFsMAX2BPUShEdKtT4HC00oyG7YjGnwBME+RzKsVndXmzryxkE0AdwIPc0DpXSPICw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"017847eeb8584d6241ad13fb7a0e1f153ada45b6a1e297d1b2f8ced2478fc2eb","last_reissued_at":"2026-05-18T03:16:38.275069Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:38.275069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.3688","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":"2026-05-18T03:16:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TbH+IdfpUG+S9NVeStk5EWVOIqVczfCjQm3TqyEE+d8PXMtACxTiGFaZxUlovCZWThcSrCvOaDHTEQl58TYmBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T00:14:59.802646Z"},"content_sha256":"d4f7a7d8feef87258e9f15de4956d9087eb64aea82eeced32f43c02357ed7256","schema_version":"1.0","event_id":"sha256:d4f7a7d8feef87258e9f15de4956d9087eb64aea82eeced32f43c02357ed7256"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:AF4EP3VYLBGWEQNNCP5XUDQ7CU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Thinnest Path Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.NI","authors_text":"Ananthram Swami, Jianhang Gao, Qing Zhao","submitted_at":"2013-05-16T06:17:51Z","abstract_excerpt":"We formulate and study the thinnest path problem in wireless ad hoc networks. The objective is to find a path from a source to its destination that results in the minimum number of nodes overhearing the message by a judicious choice of relaying nodes and their corresponding transmission power. We adopt a directed hypergraph model of the problem and establish the NP-completeness of the problem in 2-D networks. We then develop two polynomial-time approximation algorithms that offer $\\sqrt{\\frac{n}{2}}$ and $\\frac{n}{2\\sqrt{n-1}}$ approximation ratios for general directed hypergraphs (which can m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3688","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":"2026-05-18T03:16:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ol5lub5k7MswiEo+fUD4ZAjzth4ycya2EoBxxS9ms+oM6mSfUIdRJmfR8BbPNQY96khO8slK8oIdoyqkVRjsBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T00:14:59.803370Z"},"content_sha256":"3ad00cdc7d811a49f75800e241e2052d3d4611d944ae7ed5ca8fd69605ccd5f7","schema_version":"1.0","event_id":"sha256:3ad00cdc7d811a49f75800e241e2052d3d4611d944ae7ed5ca8fd69605ccd5f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AF4EP3VYLBGWEQNNCP5XUDQ7CU/bundle.json","state_url":"https://pith.science/pith/AF4EP3VYLBGWEQNNCP5XUDQ7CU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AF4EP3VYLBGWEQNNCP5XUDQ7CU/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":"2026-06-08T00:14:59Z","links":{"resolver":"https://pith.science/pith/AF4EP3VYLBGWEQNNCP5XUDQ7CU","bundle":"https://pith.science/pith/AF4EP3VYLBGWEQNNCP5XUDQ7CU/bundle.json","state":"https://pith.science/pith/AF4EP3VYLBGWEQNNCP5XUDQ7CU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AF4EP3VYLBGWEQNNCP5XUDQ7CU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AF4EP3VYLBGWEQNNCP5XUDQ7CU","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":"6b1c641722323391b580a6fd30fee52ffc8831ce978ec7a45263938f1e870cb7","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2013-05-16T06:17:51Z","title_canon_sha256":"71bb65906c38ccee776ba52314650ce33b53a4f26ff15c96403f97f0a98b8f44"},"schema_version":"1.0","source":{"id":"1305.3688","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.3688","created_at":"2026-05-18T03:16:38Z"},{"alias_kind":"arxiv_version","alias_value":"1305.3688v2","created_at":"2026-05-18T03:16:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3688","created_at":"2026-05-18T03:16:38Z"},{"alias_kind":"pith_short_12","alias_value":"AF4EP3VYLBGW","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AF4EP3VYLBGWEQNN","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AF4EP3VY","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:3ad00cdc7d811a49f75800e241e2052d3d4611d944ae7ed5ca8fd69605ccd5f7","target":"graph","created_at":"2026-05-18T03:16:38Z","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 formulate and study the thinnest path problem in wireless ad hoc networks. The objective is to find a path from a source to its destination that results in the minimum number of nodes overhearing the message by a judicious choice of relaying nodes and their corresponding transmission power. We adopt a directed hypergraph model of the problem and establish the NP-completeness of the problem in 2-D networks. We then develop two polynomial-time approximation algorithms that offer $\\sqrt{\\frac{n}{2}}$ and $\\frac{n}{2\\sqrt{n-1}}$ approximation ratios for general directed hypergraphs (which can m","authors_text":"Ananthram Swami, Jianhang Gao, Qing Zhao","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2013-05-16T06:17:51Z","title":"The Thinnest Path Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3688","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:d4f7a7d8feef87258e9f15de4956d9087eb64aea82eeced32f43c02357ed7256","target":"record","created_at":"2026-05-18T03:16:38Z","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":"6b1c641722323391b580a6fd30fee52ffc8831ce978ec7a45263938f1e870cb7","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2013-05-16T06:17:51Z","title_canon_sha256":"71bb65906c38ccee776ba52314650ce33b53a4f26ff15c96403f97f0a98b8f44"},"schema_version":"1.0","source":{"id":"1305.3688","kind":"arxiv","version":2}},"canonical_sha256":"017847eeb8584d6241ad13fb7a0e1f153ada45b6a1e297d1b2f8ced2478fc2eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"017847eeb8584d6241ad13fb7a0e1f153ada45b6a1e297d1b2f8ced2478fc2eb","first_computed_at":"2026-05-18T03:16:38.275069Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:38.275069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XMlpVfKEWjVtJQ6i1ZvaDFsMAX2BPUShEdKtT4HC00oyG7YjGnwBME+RzKsVndXmzryxkE0AdwIPc0DpXSPICw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:38.275541Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.3688","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4f7a7d8feef87258e9f15de4956d9087eb64aea82eeced32f43c02357ed7256","sha256:3ad00cdc7d811a49f75800e241e2052d3d4611d944ae7ed5ca8fd69605ccd5f7"],"state_sha256":"4d00c14d89b26886c53b0c113df66c9ae2c128464ce14c6818510b20142fe749"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LzQBrfwCWUA+PzyrrPBvECeGabpt0o729VvpEUBPZ6QWXCPEFuVrl2qJDbY90k2YUsZ0jtCgHSC70XrKbIMaCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T00:14:59.807512Z","bundle_sha256":"a429951ba91fb3c29cfa37deccad7a14a275cc72062eba072edf8614f598e914"}}