{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:X2C54HJ6VQQANEQRJUZT7GHOJI","short_pith_number":"pith:X2C54HJ6","canonical_record":{"source":{"id":"1602.01154","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2016-02-02T23:43:05Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"3887b2f7a280fef77286838ba1bb55b02342a4443d60af60c27503e4a030406a","abstract_canon_sha256":"29e8363ef5bff8a3f34c9150c98f468265226e569af93971590d858b19b0c724"},"schema_version":"1.0"},"canonical_sha256":"be85de1d3eac200692114d333f98ee4a398c41922084a4d2148405371036b710","source":{"kind":"arxiv","id":"1602.01154","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.01154","created_at":"2026-05-18T01:01:36Z"},{"alias_kind":"arxiv_version","alias_value":"1602.01154v3","created_at":"2026-05-18T01:01:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01154","created_at":"2026-05-18T01:01:36Z"},{"alias_kind":"pith_short_12","alias_value":"X2C54HJ6VQQA","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"X2C54HJ6VQQANEQR","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"X2C54HJ6","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:X2C54HJ6VQQANEQRJUZT7GHOJI","target":"record","payload":{"canonical_record":{"source":{"id":"1602.01154","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2016-02-02T23:43:05Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"3887b2f7a280fef77286838ba1bb55b02342a4443d60af60c27503e4a030406a","abstract_canon_sha256":"29e8363ef5bff8a3f34c9150c98f468265226e569af93971590d858b19b0c724"},"schema_version":"1.0"},"canonical_sha256":"be85de1d3eac200692114d333f98ee4a398c41922084a4d2148405371036b710","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:36.027538Z","signature_b64":"CeEO3VuWGiylWiMat3lD61A/feJT2n0WfiOPvg8iqAsjqq/yTmr2seA9p20ksfEd8FumrDSK3b6W381GO+LqDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be85de1d3eac200692114d333f98ee4a398c41922084a4d2148405371036b710","last_reissued_at":"2026-05-18T01:01:36.026990Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:36.026990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.01154","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:01:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tf2/dI//+JG1NTunRtcjTOZMXp4qckg/RX64Pwss4UtpfKyWsIS4C3fw72BXCKkWAwVlURiexKHSy4K22ZkmCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T09:25:33.347877Z"},"content_sha256":"788bded911c13eaf17c582a500fb555e4e5c93d785f83acad9dcaa3860b9922f","schema_version":"1.0","event_id":"sha256:788bded911c13eaf17c582a500fb555e4e5c93d785f83acad9dcaa3860b9922f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:X2C54HJ6VQQANEQRJUZT7GHOJI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The value of Side Information in Secondary Spectrum Markets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.GT","authors_text":"Arnob Ghosh, Randall Berry, Saswati Sarkar","submitted_at":"2016-02-02T23:43:05Z","abstract_excerpt":"In a secondary spectrum market primaries set prices for their unused channels to the secondaries. The payoff of a primary depends on the availability of unused channels of its competitors. We consider a model were a primary can acquire its competitor's channel state information (C-CSI) at a cost. We formulate a game between two primaries where each primary decides whether to acquire C-CSI or not and then selects its price based on that. We first characterize the Nash Equilibrium (NE) of this game for a symmetric model where the C-CSI is perfect. We show that the payoff of a primary is independ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01154","kind":"arxiv","version":3},"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":"2026-05-18T01:01:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HOG0GXi6busBk9FBgd9TPj1t0AM45HfRX2QqYS/eNnh5EyGJVz/b98Y6P8KiuVpV9oWZOXIuMQSMRBNuBWpUDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T09:25:33.348218Z"},"content_sha256":"4099788562c73def7fb948d5397521c70c69c5ab0a76f1a6b71ea7da0d215568","schema_version":"1.0","event_id":"sha256:4099788562c73def7fb948d5397521c70c69c5ab0a76f1a6b71ea7da0d215568"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X2C54HJ6VQQANEQRJUZT7GHOJI/bundle.json","state_url":"https://pith.science/pith/X2C54HJ6VQQANEQRJUZT7GHOJI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X2C54HJ6VQQANEQRJUZT7GHOJI/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":"2026-06-08T09:25:33Z","links":{"resolver":"https://pith.science/pith/X2C54HJ6VQQANEQRJUZT7GHOJI","bundle":"https://pith.science/pith/X2C54HJ6VQQANEQRJUZT7GHOJI/bundle.json","state":"https://pith.science/pith/X2C54HJ6VQQANEQRJUZT7GHOJI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X2C54HJ6VQQANEQRJUZT7GHOJI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:X2C54HJ6VQQANEQRJUZT7GHOJI","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":"29e8363ef5bff8a3f34c9150c98f468265226e569af93971590d858b19b0c724","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2016-02-02T23:43:05Z","title_canon_sha256":"3887b2f7a280fef77286838ba1bb55b02342a4443d60af60c27503e4a030406a"},"schema_version":"1.0","source":{"id":"1602.01154","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.01154","created_at":"2026-05-18T01:01:36Z"},{"alias_kind":"arxiv_version","alias_value":"1602.01154v3","created_at":"2026-05-18T01:01:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01154","created_at":"2026-05-18T01:01:36Z"},{"alias_kind":"pith_short_12","alias_value":"X2C54HJ6VQQA","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"X2C54HJ6VQQANEQR","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"X2C54HJ6","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:4099788562c73def7fb948d5397521c70c69c5ab0a76f1a6b71ea7da0d215568","target":"graph","created_at":"2026-05-18T01:01:36Z","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 secondary spectrum market primaries set prices for their unused channels to the secondaries. The payoff of a primary depends on the availability of unused channels of its competitors. We consider a model were a primary can acquire its competitor's channel state information (C-CSI) at a cost. We formulate a game between two primaries where each primary decides whether to acquire C-CSI or not and then selects its price based on that. We first characterize the Nash Equilibrium (NE) of this game for a symmetric model where the C-CSI is perfect. We show that the payoff of a primary is independ","authors_text":"Arnob Ghosh, Randall Berry, Saswati Sarkar","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2016-02-02T23:43:05Z","title":"The value of Side Information in Secondary Spectrum Markets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01154","kind":"arxiv","version":3},"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":"sha256:788bded911c13eaf17c582a500fb555e4e5c93d785f83acad9dcaa3860b9922f","target":"record","created_at":"2026-05-18T01:01:36Z","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":"29e8363ef5bff8a3f34c9150c98f468265226e569af93971590d858b19b0c724","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2016-02-02T23:43:05Z","title_canon_sha256":"3887b2f7a280fef77286838ba1bb55b02342a4443d60af60c27503e4a030406a"},"schema_version":"1.0","source":{"id":"1602.01154","kind":"arxiv","version":3}},"canonical_sha256":"be85de1d3eac200692114d333f98ee4a398c41922084a4d2148405371036b710","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be85de1d3eac200692114d333f98ee4a398c41922084a4d2148405371036b710","first_computed_at":"2026-05-18T01:01:36.026990Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:36.026990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CeEO3VuWGiylWiMat3lD61A/feJT2n0WfiOPvg8iqAsjqq/yTmr2seA9p20ksfEd8FumrDSK3b6W381GO+LqDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:36.027538Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.01154","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:788bded911c13eaf17c582a500fb555e4e5c93d785f83acad9dcaa3860b9922f","sha256:4099788562c73def7fb948d5397521c70c69c5ab0a76f1a6b71ea7da0d215568"],"state_sha256":"e2f6eff95d3060176a2405c41cc88af1b9d802af4569850c4fb64c8409a6a880"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rQcE4kPuGhbnttGdP4cO3amCInzUOPDruhlvnfC8YEuC5ar8XyTTJLDm3aurUTO6OgEM5JPec6jjL3R0rNvABA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T09:25:33.350090Z","bundle_sha256":"50d56aef7ffd919f7dcf70ebd91a9c5a9d8caa81cc323ce7c2e5b77de26f238c"}}