{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:SH7V6SYJXUYFD44WE2M2HYGZNL","short_pith_number":"pith:SH7V6SYJ","canonical_record":{"source":{"id":"1105.4143","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-05-20T18:04:53Z","cross_cats_sorted":["cs.IT","cs.NI","math.IT"],"title_canon_sha256":"94731e4207bb51501aa7a5b6155219ba350ab6d4acdb85fe82f695d97758a880","abstract_canon_sha256":"06ef1421a17fd110a5af0a870fb43ce7005d9f865b16d33a93f45620b397a848"},"schema_version":"1.0"},"canonical_sha256":"91ff5f4b09bd3051f3962699a3e0d96ae34eafb666d50e27ce687fa56eb25c93","source":{"kind":"arxiv","id":"1105.4143","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4143","created_at":"2026-05-18T02:21:52Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4143v2","created_at":"2026-05-18T02:21:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4143","created_at":"2026-05-18T02:21:52Z"},{"alias_kind":"pith_short_12","alias_value":"SH7V6SYJXUYF","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SH7V6SYJXUYFD44W","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SH7V6SYJ","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:SH7V6SYJXUYFD44WE2M2HYGZNL","target":"record","payload":{"canonical_record":{"source":{"id":"1105.4143","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-05-20T18:04:53Z","cross_cats_sorted":["cs.IT","cs.NI","math.IT"],"title_canon_sha256":"94731e4207bb51501aa7a5b6155219ba350ab6d4acdb85fe82f695d97758a880","abstract_canon_sha256":"06ef1421a17fd110a5af0a870fb43ce7005d9f865b16d33a93f45620b397a848"},"schema_version":"1.0"},"canonical_sha256":"91ff5f4b09bd3051f3962699a3e0d96ae34eafb666d50e27ce687fa56eb25c93","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:52.142360Z","signature_b64":"L1IFLCI1fWStgVastAEp/WuqHwIl/62jcWOi3ShcBu2o+jQVe02D/9OLb432vcTvq+NOC+IkO/LpiJ2Zj/XYBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91ff5f4b09bd3051f3962699a3e0d96ae34eafb666d50e27ce687fa56eb25c93","last_reissued_at":"2026-05-18T02:21:52.141641Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:52.141641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.4143","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":"2026-05-18T02:21:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2ISO8yDjetKQOj60O7LizIpBjIJQOiSXxdDYxsqQba4kigV3DfWMY0UvKacXk3MEkpGXK6+WADKs+oho4pZBDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:17:03.658756Z"},"content_sha256":"5fff0682e7665a25bf2d8acf2681edf58017f929e9902747f542c57a918b7551","schema_version":"1.0","event_id":"sha256:5fff0682e7665a25bf2d8acf2681edf58017f929e9902747f542c57a918b7551"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:SH7V6SYJXUYFD44WE2M2HYGZNL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Opportunities for Network Coding: To Wait or Not to Wait","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.NI","math.IT"],"primary_cat":"math.OC","authors_text":"Alex Sprintson, Natarajan Gautam, Navid Abedini, Srinivas Shakkottai, Yu-Pin Hsu","submitted_at":"2011-05-20T18:04:53Z","abstract_excerpt":"It has been well established that wireless network coding can significantly improve the efficiency of multi-hop wireless networks. However, in a stochastic environment some of the packets might not have coding pairs, which limits the number of available coding opportunities. In this context, an important decision is whether to delay packet transmission in hope that a coding pair will be available in the future or transmit a packet without coding. The paper addresses this problem by formulating a stochastic dynamic program whose objective is to minimize the long-run average cost per unit time i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4143","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":"2026-05-18T02:21:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tljTEVfvoO02GT2e7pLtNMp+mI4/jfso1ZoaCoIDKkcnI5BaxuZDi8IWZuXfPyKKik4m0o5k8/eVLbe9dsmVCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:17:03.659108Z"},"content_sha256":"ff0a9057d4fa8819fb7dd2c3a0f8a4972c61acbdaa9e6228aff39e70c02c5621","schema_version":"1.0","event_id":"sha256:ff0a9057d4fa8819fb7dd2c3a0f8a4972c61acbdaa9e6228aff39e70c02c5621"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SH7V6SYJXUYFD44WE2M2HYGZNL/bundle.json","state_url":"https://pith.science/pith/SH7V6SYJXUYFD44WE2M2HYGZNL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SH7V6SYJXUYFD44WE2M2HYGZNL/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":"2026-06-02T13:17:03Z","links":{"resolver":"https://pith.science/pith/SH7V6SYJXUYFD44WE2M2HYGZNL","bundle":"https://pith.science/pith/SH7V6SYJXUYFD44WE2M2HYGZNL/bundle.json","state":"https://pith.science/pith/SH7V6SYJXUYFD44WE2M2HYGZNL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SH7V6SYJXUYFD44WE2M2HYGZNL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SH7V6SYJXUYFD44WE2M2HYGZNL","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":"06ef1421a17fd110a5af0a870fb43ce7005d9f865b16d33a93f45620b397a848","cross_cats_sorted":["cs.IT","cs.NI","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-05-20T18:04:53Z","title_canon_sha256":"94731e4207bb51501aa7a5b6155219ba350ab6d4acdb85fe82f695d97758a880"},"schema_version":"1.0","source":{"id":"1105.4143","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4143","created_at":"2026-05-18T02:21:52Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4143v2","created_at":"2026-05-18T02:21:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4143","created_at":"2026-05-18T02:21:52Z"},{"alias_kind":"pith_short_12","alias_value":"SH7V6SYJXUYF","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SH7V6SYJXUYFD44W","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SH7V6SYJ","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:ff0a9057d4fa8819fb7dd2c3a0f8a4972c61acbdaa9e6228aff39e70c02c5621","target":"graph","created_at":"2026-05-18T02:21:52Z","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":"It has been well established that wireless network coding can significantly improve the efficiency of multi-hop wireless networks. However, in a stochastic environment some of the packets might not have coding pairs, which limits the number of available coding opportunities. In this context, an important decision is whether to delay packet transmission in hope that a coding pair will be available in the future or transmit a packet without coding. The paper addresses this problem by formulating a stochastic dynamic program whose objective is to minimize the long-run average cost per unit time i","authors_text":"Alex Sprintson, Natarajan Gautam, Navid Abedini, Srinivas Shakkottai, Yu-Pin Hsu","cross_cats":["cs.IT","cs.NI","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-05-20T18:04:53Z","title":"Opportunities for Network Coding: To Wait or Not to Wait"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4143","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":"sha256:5fff0682e7665a25bf2d8acf2681edf58017f929e9902747f542c57a918b7551","target":"record","created_at":"2026-05-18T02:21:52Z","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":"06ef1421a17fd110a5af0a870fb43ce7005d9f865b16d33a93f45620b397a848","cross_cats_sorted":["cs.IT","cs.NI","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-05-20T18:04:53Z","title_canon_sha256":"94731e4207bb51501aa7a5b6155219ba350ab6d4acdb85fe82f695d97758a880"},"schema_version":"1.0","source":{"id":"1105.4143","kind":"arxiv","version":2}},"canonical_sha256":"91ff5f4b09bd3051f3962699a3e0d96ae34eafb666d50e27ce687fa56eb25c93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91ff5f4b09bd3051f3962699a3e0d96ae34eafb666d50e27ce687fa56eb25c93","first_computed_at":"2026-05-18T02:21:52.141641Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:52.141641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L1IFLCI1fWStgVastAEp/WuqHwIl/62jcWOi3ShcBu2o+jQVe02D/9OLb432vcTvq+NOC+IkO/LpiJ2Zj/XYBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:52.142360Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.4143","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5fff0682e7665a25bf2d8acf2681edf58017f929e9902747f542c57a918b7551","sha256:ff0a9057d4fa8819fb7dd2c3a0f8a4972c61acbdaa9e6228aff39e70c02c5621"],"state_sha256":"ed61bd0e8e9801d792691cf36721265ee43e0ae8995831e729899e10b4953ea8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MF/ND1Y14Dn8ZHMM/ZsF9+3PVtbb+pJJ0BKRUFTL9GOBB5Y2ZA5VlaL9MjSOtLkzLoXZ+sP3sYnKL/R4MvF9AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T13:17:03.661149Z","bundle_sha256":"1292181848000087acb99a99953740cee391f8a520f865b6c48f843db571fe9b"}}