{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZYY6OPEOC6RNIOH6JG7AT4SDFX","short_pith_number":"pith:ZYY6OPEO","canonical_record":{"source":{"id":"1509.01313","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-09-04T00:25:07Z","cross_cats_sorted":["cs.GT","math.OC"],"title_canon_sha256":"5778bf581bfdd9d81b524345aa9a13b6c2f17f62ec00606c09534b6dabba0758","abstract_canon_sha256":"68cce5fd35307b8e2d2537bd162fa6d4d39f972175bee5da177768e62031134a"},"schema_version":"1.0"},"canonical_sha256":"ce31e73c8e17a2d438fe49be09f2432ddc1d0c5398f1c6fef3446333e5492012","source":{"kind":"arxiv","id":"1509.01313","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01313","created_at":"2026-05-18T01:23:44Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01313v2","created_at":"2026-05-18T01:23:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01313","created_at":"2026-05-18T01:23:44Z"},{"alias_kind":"pith_short_12","alias_value":"ZYY6OPEOC6RN","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZYY6OPEOC6RNIOH6","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZYY6OPEO","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZYY6OPEOC6RNIOH6JG7AT4SDFX","target":"record","payload":{"canonical_record":{"source":{"id":"1509.01313","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-09-04T00:25:07Z","cross_cats_sorted":["cs.GT","math.OC"],"title_canon_sha256":"5778bf581bfdd9d81b524345aa9a13b6c2f17f62ec00606c09534b6dabba0758","abstract_canon_sha256":"68cce5fd35307b8e2d2537bd162fa6d4d39f972175bee5da177768e62031134a"},"schema_version":"1.0"},"canonical_sha256":"ce31e73c8e17a2d438fe49be09f2432ddc1d0c5398f1c6fef3446333e5492012","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:44.513572Z","signature_b64":"6CXVQBB6d6SlbRFzSKE61PH+BBQ0UrncT1KITBxgLKtyIfIwsNDTPf38Aeobd7ZcJTFoBmC5gWhirf/cBMl5Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce31e73c8e17a2d438fe49be09f2432ddc1d0c5398f1c6fef3446333e5492012","last_reissued_at":"2026-05-18T01:23:44.512917Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:44.512917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.01313","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":"2026-05-18T01:23:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bCuzOq6WA6emD22KgdVIMKhW+JUbfqTYWd7f7YCXgDOa7cFBkIUZOqk0aOIspu75R0L7vH+9Q4rnEZO6+SYSBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:53:19.303511Z"},"content_sha256":"263262dc1caa915c18627bf26c1a0d631544fa127f1cd3f61aa8ec2145112400","schema_version":"1.0","event_id":"sha256:263262dc1caa915c18627bf26c1a0d631544fa127f1cd3f61aa8ec2145112400"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZYY6OPEOC6RNIOH6JG7AT4SDFX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamic Potential Games in Communications: Fundamentals and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT","math.OC"],"primary_cat":"cs.SY","authors_text":"Javier Zazo, Matilde S\\'anchez-Fern\\'andez, Santiago Zazo, Sergio Valcarcel Macua","submitted_at":"2015-09-04T00:25:07Z","abstract_excerpt":"In a noncooperative dynamic game, multiple agents operating in a changing environment aim to optimize their utilities over an infinite time horizon. Time-varying environments allow to model more realistic scenarios (e.g., mobile devices equipped with batteries, wireless communications over a fading channel, etc.). However, solving a dynamic game is a difficult task that requires dealing with multiple coupled optimal control problems. We focus our analysis on a class of problems, named \\textit{dynamic potential games}, whose solution can be found through a single multivariate optimal control pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01313","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":"2026-05-18T01:23:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sqgjtMa+0nBeuPraY3AMX6qMhlDdagnEMmv+8WljM4O/ZHcpr2NdLy1iz4GqHkN8npJpPMM0HI20PMjg3kmPDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:53:19.304087Z"},"content_sha256":"130d6f887363d562a2d9b15e4030e93d9cedab7e63407deed3d17c6c0061366f","schema_version":"1.0","event_id":"sha256:130d6f887363d562a2d9b15e4030e93d9cedab7e63407deed3d17c6c0061366f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZYY6OPEOC6RNIOH6JG7AT4SDFX/bundle.json","state_url":"https://pith.science/pith/ZYY6OPEOC6RNIOH6JG7AT4SDFX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZYY6OPEOC6RNIOH6JG7AT4SDFX/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":"2026-05-26T16:53:19Z","links":{"resolver":"https://pith.science/pith/ZYY6OPEOC6RNIOH6JG7AT4SDFX","bundle":"https://pith.science/pith/ZYY6OPEOC6RNIOH6JG7AT4SDFX/bundle.json","state":"https://pith.science/pith/ZYY6OPEOC6RNIOH6JG7AT4SDFX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZYY6OPEOC6RNIOH6JG7AT4SDFX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZYY6OPEOC6RNIOH6JG7AT4SDFX","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":"68cce5fd35307b8e2d2537bd162fa6d4d39f972175bee5da177768e62031134a","cross_cats_sorted":["cs.GT","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-09-04T00:25:07Z","title_canon_sha256":"5778bf581bfdd9d81b524345aa9a13b6c2f17f62ec00606c09534b6dabba0758"},"schema_version":"1.0","source":{"id":"1509.01313","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01313","created_at":"2026-05-18T01:23:44Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01313v2","created_at":"2026-05-18T01:23:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01313","created_at":"2026-05-18T01:23:44Z"},{"alias_kind":"pith_short_12","alias_value":"ZYY6OPEOC6RN","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZYY6OPEOC6RNIOH6","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZYY6OPEO","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:130d6f887363d562a2d9b15e4030e93d9cedab7e63407deed3d17c6c0061366f","target":"graph","created_at":"2026-05-18T01:23:44Z","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":"In a noncooperative dynamic game, multiple agents operating in a changing environment aim to optimize their utilities over an infinite time horizon. Time-varying environments allow to model more realistic scenarios (e.g., mobile devices equipped with batteries, wireless communications over a fading channel, etc.). However, solving a dynamic game is a difficult task that requires dealing with multiple coupled optimal control problems. We focus our analysis on a class of problems, named \\textit{dynamic potential games}, whose solution can be found through a single multivariate optimal control pr","authors_text":"Javier Zazo, Matilde S\\'anchez-Fern\\'andez, Santiago Zazo, Sergio Valcarcel Macua","cross_cats":["cs.GT","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-09-04T00:25:07Z","title":"Dynamic Potential Games in Communications: Fundamentals and Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01313","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":"sha256:263262dc1caa915c18627bf26c1a0d631544fa127f1cd3f61aa8ec2145112400","target":"record","created_at":"2026-05-18T01:23:44Z","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":"68cce5fd35307b8e2d2537bd162fa6d4d39f972175bee5da177768e62031134a","cross_cats_sorted":["cs.GT","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-09-04T00:25:07Z","title_canon_sha256":"5778bf581bfdd9d81b524345aa9a13b6c2f17f62ec00606c09534b6dabba0758"},"schema_version":"1.0","source":{"id":"1509.01313","kind":"arxiv","version":2}},"canonical_sha256":"ce31e73c8e17a2d438fe49be09f2432ddc1d0c5398f1c6fef3446333e5492012","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce31e73c8e17a2d438fe49be09f2432ddc1d0c5398f1c6fef3446333e5492012","first_computed_at":"2026-05-18T01:23:44.512917Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:44.512917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6CXVQBB6d6SlbRFzSKE61PH+BBQ0UrncT1KITBxgLKtyIfIwsNDTPf38Aeobd7ZcJTFoBmC5gWhirf/cBMl5Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:44.513572Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.01313","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:263262dc1caa915c18627bf26c1a0d631544fa127f1cd3f61aa8ec2145112400","sha256:130d6f887363d562a2d9b15e4030e93d9cedab7e63407deed3d17c6c0061366f"],"state_sha256":"cd5cc4ad31568d5cd904d8244ab1f1646d113461b7542601f7f2d26f501e4f53"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IOaFyyzJNKoyC3CY0cimyy8DOiqe4hoK7nRLTqlRAzTCc4+gmOPlkXwFB2yd2WHx/Omugf8sHZaPGWyTjmbPAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T16:53:19.307403Z","bundle_sha256":"7ad6ac0c6e0d227f17507b8bd4ad9b20c069cea8bd0dc06b58d4ff6711eb2999"}}