{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:RHDZPUJYR5TEUXSGU2IUXHK7NC","short_pith_number":"pith:RHDZPUJY","canonical_record":{"source":{"id":"1307.8410","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2013-07-31T18:07:24Z","cross_cats_sorted":["cs.IT","math.IT","math.PR"],"title_canon_sha256":"25d93234e19861296775b2ecea4410e7b9c9fae2c7bcdfa6cd6eb8b6e2e9d27c","abstract_canon_sha256":"59763bfc5bb3b4e502caaf015d6fd3b01fce27abd752582631a5bcd6c5a769d3"},"schema_version":"1.0"},"canonical_sha256":"89c797d1388f664a5e46a6914b9d5f68a4501e6a9da76f9fb3a4ebf967d2b852","source":{"kind":"arxiv","id":"1307.8410","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.8410","created_at":"2026-05-18T03:17:01Z"},{"alias_kind":"arxiv_version","alias_value":"1307.8410v1","created_at":"2026-05-18T03:17:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.8410","created_at":"2026-05-18T03:17:01Z"},{"alias_kind":"pith_short_12","alias_value":"RHDZPUJYR5TE","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"RHDZPUJYR5TEUXSG","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"RHDZPUJY","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:RHDZPUJYR5TEUXSGU2IUXHK7NC","target":"record","payload":{"canonical_record":{"source":{"id":"1307.8410","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2013-07-31T18:07:24Z","cross_cats_sorted":["cs.IT","math.IT","math.PR"],"title_canon_sha256":"25d93234e19861296775b2ecea4410e7b9c9fae2c7bcdfa6cd6eb8b6e2e9d27c","abstract_canon_sha256":"59763bfc5bb3b4e502caaf015d6fd3b01fce27abd752582631a5bcd6c5a769d3"},"schema_version":"1.0"},"canonical_sha256":"89c797d1388f664a5e46a6914b9d5f68a4501e6a9da76f9fb3a4ebf967d2b852","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:01.234979Z","signature_b64":"Knghb5zuqmreo9ROe2mJQhJ/+trdBi7wklQzzgC0CTfVGzsSqfwm8Vxfx+K04QdrcZsq+MXSd0wNkGomLb9ZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89c797d1388f664a5e46a6914b9d5f68a4501e6a9da76f9fb3a4ebf967d2b852","last_reissued_at":"2026-05-18T03:17:01.234438Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:01.234438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.8410","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":"2026-05-18T03:17:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8DF2tuhCWFUsegExDj1LULx9Z5Nhm69bhFgJXNPjPQMbktzvW+EoWPUPIdy0mi8opqWWbnTufb4Wiwt8Sp+JBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T11:35:36.908513Z"},"content_sha256":"27b95cceb9eed90315bd93ae997abbfa1fe5eefabbdf52413031accce2281167","schema_version":"1.0","event_id":"sha256:27b95cceb9eed90315bd93ae997abbfa1fe5eefabbdf52413031accce2281167"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:RHDZPUJYR5TEUXSGU2IUXHK7NC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analysis of a Proportionally Fair and Locally Adaptive spatial Aloha in Poisson Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.PR"],"primary_cat":"cs.NI","authors_text":"Bartlomiej Blaszczyszyn (INRIA Rocquencourt), Chandramani Singh (INRIA Rocquencourt), Fran\\c{c}ois Baccelli (INRIA Rocquencourt, LINCS)","submitted_at":"2013-07-31T18:07:24Z","abstract_excerpt":"The proportionally fair sharing of the capacity of a Poisson network using Spatial-Aloha leads to closed-form performance expressions in two extreme cases: (1) the case without topology information, where the analysis boils down to a parametric optimization problem leveraging stochastic geometry; (2) the case with full network topology information, which was recently solved using shot-noise techniques. We show that there exists a continuum of adaptive controls between these two extremes, based on local stopping sets, which can also be analyzed in closed form. We also show that these control sc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.8410","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":"2026-05-18T03:17:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nXpUHHMMZQX4OVSZ5vq1WvAt7PA5en8V+dzB6S4hQ2QR/PSK52o6SVFJRtC78Uasmq84+duP1xXTBf4G4TmZAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T11:35:36.909237Z"},"content_sha256":"ac171dab178f224078ff70e33d38e3630ca8ec0f54dcf4c914481fc97585e468","schema_version":"1.0","event_id":"sha256:ac171dab178f224078ff70e33d38e3630ca8ec0f54dcf4c914481fc97585e468"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RHDZPUJYR5TEUXSGU2IUXHK7NC/bundle.json","state_url":"https://pith.science/pith/RHDZPUJYR5TEUXSGU2IUXHK7NC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RHDZPUJYR5TEUXSGU2IUXHK7NC/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":"2026-05-23T11:35:36Z","links":{"resolver":"https://pith.science/pith/RHDZPUJYR5TEUXSGU2IUXHK7NC","bundle":"https://pith.science/pith/RHDZPUJYR5TEUXSGU2IUXHK7NC/bundle.json","state":"https://pith.science/pith/RHDZPUJYR5TEUXSGU2IUXHK7NC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RHDZPUJYR5TEUXSGU2IUXHK7NC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RHDZPUJYR5TEUXSGU2IUXHK7NC","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":"59763bfc5bb3b4e502caaf015d6fd3b01fce27abd752582631a5bcd6c5a769d3","cross_cats_sorted":["cs.IT","math.IT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2013-07-31T18:07:24Z","title_canon_sha256":"25d93234e19861296775b2ecea4410e7b9c9fae2c7bcdfa6cd6eb8b6e2e9d27c"},"schema_version":"1.0","source":{"id":"1307.8410","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.8410","created_at":"2026-05-18T03:17:01Z"},{"alias_kind":"arxiv_version","alias_value":"1307.8410v1","created_at":"2026-05-18T03:17:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.8410","created_at":"2026-05-18T03:17:01Z"},{"alias_kind":"pith_short_12","alias_value":"RHDZPUJYR5TE","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"RHDZPUJYR5TEUXSG","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"RHDZPUJY","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:ac171dab178f224078ff70e33d38e3630ca8ec0f54dcf4c914481fc97585e468","target":"graph","created_at":"2026-05-18T03:17:01Z","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":"The proportionally fair sharing of the capacity of a Poisson network using Spatial-Aloha leads to closed-form performance expressions in two extreme cases: (1) the case without topology information, where the analysis boils down to a parametric optimization problem leveraging stochastic geometry; (2) the case with full network topology information, which was recently solved using shot-noise techniques. We show that there exists a continuum of adaptive controls between these two extremes, based on local stopping sets, which can also be analyzed in closed form. We also show that these control sc","authors_text":"Bartlomiej Blaszczyszyn (INRIA Rocquencourt), Chandramani Singh (INRIA Rocquencourt), Fran\\c{c}ois Baccelli (INRIA Rocquencourt, LINCS)","cross_cats":["cs.IT","math.IT","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2013-07-31T18:07:24Z","title":"Analysis of a Proportionally Fair and Locally Adaptive spatial Aloha in Poisson Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.8410","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":"sha256:27b95cceb9eed90315bd93ae997abbfa1fe5eefabbdf52413031accce2281167","target":"record","created_at":"2026-05-18T03:17:01Z","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":"59763bfc5bb3b4e502caaf015d6fd3b01fce27abd752582631a5bcd6c5a769d3","cross_cats_sorted":["cs.IT","math.IT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2013-07-31T18:07:24Z","title_canon_sha256":"25d93234e19861296775b2ecea4410e7b9c9fae2c7bcdfa6cd6eb8b6e2e9d27c"},"schema_version":"1.0","source":{"id":"1307.8410","kind":"arxiv","version":1}},"canonical_sha256":"89c797d1388f664a5e46a6914b9d5f68a4501e6a9da76f9fb3a4ebf967d2b852","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89c797d1388f664a5e46a6914b9d5f68a4501e6a9da76f9fb3a4ebf967d2b852","first_computed_at":"2026-05-18T03:17:01.234438Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:01.234438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Knghb5zuqmreo9ROe2mJQhJ/+trdBi7wklQzzgC0CTfVGzsSqfwm8Vxfx+K04QdrcZsq+MXSd0wNkGomLb9ZDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:01.234979Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.8410","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27b95cceb9eed90315bd93ae997abbfa1fe5eefabbdf52413031accce2281167","sha256:ac171dab178f224078ff70e33d38e3630ca8ec0f54dcf4c914481fc97585e468"],"state_sha256":"4efe081153973943f65d5df559b0785783029d9accacec21ba1b247bac0ef0e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kmP+d3l+BLJHedr/HeSyBL0Ium17jlL9jpznt4wqBMd/w6/CkfPyk+t5YPVwU4oeCumM6SqEdTV5hp3R8mIqAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T11:35:36.913478Z","bundle_sha256":"43175f5847721bac34d343d5e05f97ca38813864f4d9d941847ca574cb23aa56"}}