{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:EEKQEIHKDWVUS6G3H6G6EY5JBL","short_pith_number":"pith:EEKQEIHK","canonical_record":{"source":{"id":"1202.6348","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-02-28T20:28:11Z","cross_cats_sorted":["cond-mat.stat-mech","cs.SI","math.IT"],"title_canon_sha256":"23d56031d84889ea767d2ae4ea5ed50e634eb7b52a0b720f879de619ab92f813","abstract_canon_sha256":"4f10e9b6699e148b58d2d421feae50a879bde567ad7814411dcc9dab19d99716"},"schema_version":"1.0"},"canonical_sha256":"21150220ea1dab4978db3f8de263a90ad5b7e75aea228ccecf68ec07b58cb9f3","source":{"kind":"arxiv","id":"1202.6348","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.6348","created_at":"2026-05-18T03:02:17Z"},{"alias_kind":"arxiv_version","alias_value":"1202.6348v2","created_at":"2026-05-18T03:02:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.6348","created_at":"2026-05-18T03:02:17Z"},{"alias_kind":"pith_short_12","alias_value":"EEKQEIHKDWVU","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EEKQEIHKDWVUS6G3","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EEKQEIHK","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:EEKQEIHKDWVUS6G3H6G6EY5JBL","target":"record","payload":{"canonical_record":{"source":{"id":"1202.6348","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-02-28T20:28:11Z","cross_cats_sorted":["cond-mat.stat-mech","cs.SI","math.IT"],"title_canon_sha256":"23d56031d84889ea767d2ae4ea5ed50e634eb7b52a0b720f879de619ab92f813","abstract_canon_sha256":"4f10e9b6699e148b58d2d421feae50a879bde567ad7814411dcc9dab19d99716"},"schema_version":"1.0"},"canonical_sha256":"21150220ea1dab4978db3f8de263a90ad5b7e75aea228ccecf68ec07b58cb9f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:17.991050Z","signature_b64":"emtMcIfHlwOagu/5GDGW8e/YyOnkoNA4q1NvvavR+Dwy0j2ERXr50lahX0johe3q6tdAa72kDcK5cj+oqc8MDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21150220ea1dab4978db3f8de263a90ad5b7e75aea228ccecf68ec07b58cb9f3","last_reissued_at":"2026-05-18T03:02:17.990106Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:17.990106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.6348","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":"2026-05-18T03:02:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z+OniljI2up8u//t6eSf5t8xF0yT6hBsqA9HcgfZxDLHiUR1i4gqWI6oMsjDy7VVLnGKV/EwW+Z5Sl5DzVHYCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T07:22:01.785715Z"},"content_sha256":"dfba50c15555530e3b707eb8480787bc36d3182429257cf04c41ade4442ada14","schema_version":"1.0","event_id":"sha256:dfba50c15555530e3b707eb8480787bc36d3182429257cf04c41ade4442ada14"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:EEKQEIHKDWVUS6G3H6G6EY5JBL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Power Optimization in Random Wireless Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.SI","math.IT"],"primary_cat":"cs.IT","authors_text":"Aris L. Moustakas, Nicholas Bambos, Panayotis Mertikopoulos","submitted_at":"2012-02-28T20:28:11Z","abstract_excerpt":"Consider a wireless network of transmitter-receiver pairs where the transmitters adjust their powers to maintain a target SINR level in the presence of interference. In this paper, we analyze the optimal power vector that achieves this target in large, random networks obtained by \"erasing\" a finite fraction of nodes from a regular lattice of transmitter-receiver pairs. We show that this problem is equivalent to the so-called Anderson model of electron motion in dirty metals which has been used extensively in the analysis of diffusion in random environments. A standard approximation to this mod"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6348","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":"2026-05-18T03:02:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uPOi1Y+b5tCAzmk4qG5NQ3FkZEI8LhFSCsteUrpoCIk2NrKmqwAxv3Fi8Kdp4uiOa4794kUMowDTnOW6icOLAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T07:22:01.786098Z"},"content_sha256":"433f6ecc423c182c01ddd8ebf9f0b5b3339578cf89cbeb15b6a2ad231ef6e203","schema_version":"1.0","event_id":"sha256:433f6ecc423c182c01ddd8ebf9f0b5b3339578cf89cbeb15b6a2ad231ef6e203"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EEKQEIHKDWVUS6G3H6G6EY5JBL/bundle.json","state_url":"https://pith.science/pith/EEKQEIHKDWVUS6G3H6G6EY5JBL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EEKQEIHKDWVUS6G3H6G6EY5JBL/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":"2026-06-11T07:22:01Z","links":{"resolver":"https://pith.science/pith/EEKQEIHKDWVUS6G3H6G6EY5JBL","bundle":"https://pith.science/pith/EEKQEIHKDWVUS6G3H6G6EY5JBL/bundle.json","state":"https://pith.science/pith/EEKQEIHKDWVUS6G3H6G6EY5JBL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EEKQEIHKDWVUS6G3H6G6EY5JBL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:EEKQEIHKDWVUS6G3H6G6EY5JBL","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":"4f10e9b6699e148b58d2d421feae50a879bde567ad7814411dcc9dab19d99716","cross_cats_sorted":["cond-mat.stat-mech","cs.SI","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-02-28T20:28:11Z","title_canon_sha256":"23d56031d84889ea767d2ae4ea5ed50e634eb7b52a0b720f879de619ab92f813"},"schema_version":"1.0","source":{"id":"1202.6348","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.6348","created_at":"2026-05-18T03:02:17Z"},{"alias_kind":"arxiv_version","alias_value":"1202.6348v2","created_at":"2026-05-18T03:02:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.6348","created_at":"2026-05-18T03:02:17Z"},{"alias_kind":"pith_short_12","alias_value":"EEKQEIHKDWVU","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EEKQEIHKDWVUS6G3","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EEKQEIHK","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:433f6ecc423c182c01ddd8ebf9f0b5b3339578cf89cbeb15b6a2ad231ef6e203","target":"graph","created_at":"2026-05-18T03:02:17Z","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":"Consider a wireless network of transmitter-receiver pairs where the transmitters adjust their powers to maintain a target SINR level in the presence of interference. In this paper, we analyze the optimal power vector that achieves this target in large, random networks obtained by \"erasing\" a finite fraction of nodes from a regular lattice of transmitter-receiver pairs. We show that this problem is equivalent to the so-called Anderson model of electron motion in dirty metals which has been used extensively in the analysis of diffusion in random environments. A standard approximation to this mod","authors_text":"Aris L. Moustakas, Nicholas Bambos, Panayotis Mertikopoulos","cross_cats":["cond-mat.stat-mech","cs.SI","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-02-28T20:28:11Z","title":"Power Optimization in Random Wireless Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6348","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:dfba50c15555530e3b707eb8480787bc36d3182429257cf04c41ade4442ada14","target":"record","created_at":"2026-05-18T03:02:17Z","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":"4f10e9b6699e148b58d2d421feae50a879bde567ad7814411dcc9dab19d99716","cross_cats_sorted":["cond-mat.stat-mech","cs.SI","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-02-28T20:28:11Z","title_canon_sha256":"23d56031d84889ea767d2ae4ea5ed50e634eb7b52a0b720f879de619ab92f813"},"schema_version":"1.0","source":{"id":"1202.6348","kind":"arxiv","version":2}},"canonical_sha256":"21150220ea1dab4978db3f8de263a90ad5b7e75aea228ccecf68ec07b58cb9f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21150220ea1dab4978db3f8de263a90ad5b7e75aea228ccecf68ec07b58cb9f3","first_computed_at":"2026-05-18T03:02:17.990106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:17.990106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"emtMcIfHlwOagu/5GDGW8e/YyOnkoNA4q1NvvavR+Dwy0j2ERXr50lahX0johe3q6tdAa72kDcK5cj+oqc8MDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:17.991050Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.6348","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfba50c15555530e3b707eb8480787bc36d3182429257cf04c41ade4442ada14","sha256:433f6ecc423c182c01ddd8ebf9f0b5b3339578cf89cbeb15b6a2ad231ef6e203"],"state_sha256":"3420cae3837d9fd9e357ba0acc613bcd6eac63918e52afeddaf19e98867bace3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wsXZDvTpvdieDFyZEN2v9B9CxgHeHifMZgZepyAB2jNRKOfelV0H4yqAUsL6yY7ZpRgDhSO6tC9C9Ke4T7joDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T07:22:01.789143Z","bundle_sha256":"d843f40acf8efbd5c3e196c78dadbe8c91d48db72e74018a35d12d8f96d87376"}}