{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:DEWWOZWLQ6P7CP5BTFDBACUFTV","short_pith_number":"pith:DEWWOZWL","canonical_record":{"source":{"id":"2607.13607","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.MA","submitted_at":"2026-07-15T08:56:53Z","cross_cats_sorted":["econ.GN","econ.TH","q-fin.EC"],"title_canon_sha256":"eaa8378f7a459cbd4cd57dcb815cd4d38add0a7fe849371db70c3087f928a5c9","abstract_canon_sha256":"c9f51f0283c7476e4dc1ba378fd9ca3b2864c212015c1c75e7d6b4286238c957"},"schema_version":"1.0"},"canonical_sha256":"192d6766cb879ff13fa19946100a859d74fed6cda5739eb34d748748a70fb42b","source":{"kind":"arxiv","id":"2607.13607","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.13607","created_at":"2026-07-16T01:22:56Z"},{"alias_kind":"arxiv_version","alias_value":"2607.13607v1","created_at":"2026-07-16T01:22:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.13607","created_at":"2026-07-16T01:22:56Z"},{"alias_kind":"pith_short_12","alias_value":"DEWWOZWLQ6P7","created_at":"2026-07-16T01:22:56Z"},{"alias_kind":"pith_short_16","alias_value":"DEWWOZWLQ6P7CP5B","created_at":"2026-07-16T01:22:56Z"},{"alias_kind":"pith_short_8","alias_value":"DEWWOZWL","created_at":"2026-07-16T01:22:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:DEWWOZWLQ6P7CP5BTFDBACUFTV","target":"record","payload":{"canonical_record":{"source":{"id":"2607.13607","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.MA","submitted_at":"2026-07-15T08:56:53Z","cross_cats_sorted":["econ.GN","econ.TH","q-fin.EC"],"title_canon_sha256":"eaa8378f7a459cbd4cd57dcb815cd4d38add0a7fe849371db70c3087f928a5c9","abstract_canon_sha256":"c9f51f0283c7476e4dc1ba378fd9ca3b2864c212015c1c75e7d6b4286238c957"},"schema_version":"1.0"},"canonical_sha256":"192d6766cb879ff13fa19946100a859d74fed6cda5739eb34d748748a70fb42b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-16T01:22:56.699055Z","signature_b64":"KvvH7VSl9as6JSWrxGB+ihBwiE1WdSSAnWPNWxTQ7xE4KKDtvoO+McqQm1xGYmh5pC9+P0+vnVnaqvjp5FcSAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"192d6766cb879ff13fa19946100a859d74fed6cda5739eb34d748748a70fb42b","last_reissued_at":"2026-07-16T01:22:56.698206Z","signature_status":"signed_v1","first_computed_at":"2026-07-16T01:22:56.698206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.13607","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":"2026-07-16T01:22:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZR5YSxu9V8R97SG0v/EEWwv0w/0dtPbwT322CPKcCWEc0U5KWcSt2s7mfNj+FIbThsn9cJYe7+oArv9VpDVXAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T18:22:53.972941Z"},"content_sha256":"02f6d5aded722fc87191f1850d16c31729bec084abb69bb16a5cc51a78dffbac","schema_version":"1.0","event_id":"sha256:02f6d5aded722fc87191f1850d16c31729bec084abb69bb16a5cc51a78dffbac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:DEWWOZWLQ6P7CP5BTFDBACUFTV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equilibrium stability as a driver of cooperation among Q-learners","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["econ.GN","econ.TH","q-fin.EC"],"primary_cat":"cs.MA","authors_text":"Janusz M. Meylahn, Maximilian Sch\\\"afer","submitted_at":"2026-07-15T08:56:53Z","abstract_excerpt":"Algorithmic collusion among pricing algorithms has raised concerns about sustained supra-competitive prices and their implications for social welfare. Existing work has largely focused on the probability that reinforcement-learning algorithms converge to cooperative strategies, typically under the assumption that exploration vanishes over time. Motivated by the observation that algorithms deployed in practice are likely to continue exploring in order to remain adaptive to changing environments, we study learning dynamics under constant exploration. In this setting, the relevant question is no "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13607","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.13607/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-16T01:22:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oSZ9XzDhFVAmOh1ag5ElwsJZfWcLVmo9l0VT5893TZe2DGF4JfTPkRcbVtnxEvOkq0oKMg3rORLwCahlX5mOCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T18:22:53.973442Z"},"content_sha256":"96040924bb2523b1619be6afc51edb49ff429b934ea8aa6c09d3969a171c8d1c","schema_version":"1.0","event_id":"sha256:96040924bb2523b1619be6afc51edb49ff429b934ea8aa6c09d3969a171c8d1c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DEWWOZWLQ6P7CP5BTFDBACUFTV/bundle.json","state_url":"https://pith.science/pith/DEWWOZWLQ6P7CP5BTFDBACUFTV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DEWWOZWLQ6P7CP5BTFDBACUFTV/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":"2026-08-12T18:22:53Z","links":{"resolver":"https://pith.science/pith/DEWWOZWLQ6P7CP5BTFDBACUFTV","bundle":"https://pith.science/pith/DEWWOZWLQ6P7CP5BTFDBACUFTV/bundle.json","state":"https://pith.science/pith/DEWWOZWLQ6P7CP5BTFDBACUFTV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DEWWOZWLQ6P7CP5BTFDBACUFTV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:DEWWOZWLQ6P7CP5BTFDBACUFTV","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":"c9f51f0283c7476e4dc1ba378fd9ca3b2864c212015c1c75e7d6b4286238c957","cross_cats_sorted":["econ.GN","econ.TH","q-fin.EC"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.MA","submitted_at":"2026-07-15T08:56:53Z","title_canon_sha256":"eaa8378f7a459cbd4cd57dcb815cd4d38add0a7fe849371db70c3087f928a5c9"},"schema_version":"1.0","source":{"id":"2607.13607","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.13607","created_at":"2026-07-16T01:22:56Z"},{"alias_kind":"arxiv_version","alias_value":"2607.13607v1","created_at":"2026-07-16T01:22:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.13607","created_at":"2026-07-16T01:22:56Z"},{"alias_kind":"pith_short_12","alias_value":"DEWWOZWLQ6P7","created_at":"2026-07-16T01:22:56Z"},{"alias_kind":"pith_short_16","alias_value":"DEWWOZWLQ6P7CP5B","created_at":"2026-07-16T01:22:56Z"},{"alias_kind":"pith_short_8","alias_value":"DEWWOZWL","created_at":"2026-07-16T01:22:56Z"}],"graph_snapshots":[{"event_id":"sha256:96040924bb2523b1619be6afc51edb49ff429b934ea8aa6c09d3969a171c8d1c","target":"graph","created_at":"2026-07-16T01:22:56Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.13607/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Algorithmic collusion among pricing algorithms has raised concerns about sustained supra-competitive prices and their implications for social welfare. Existing work has largely focused on the probability that reinforcement-learning algorithms converge to cooperative strategies, typically under the assumption that exploration vanishes over time. Motivated by the observation that algorithms deployed in practice are likely to continue exploring in order to remain adaptive to changing environments, we study learning dynamics under constant exploration. In this setting, the relevant question is no ","authors_text":"Janusz M. Meylahn, Maximilian Sch\\\"afer","cross_cats":["econ.GN","econ.TH","q-fin.EC"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.MA","submitted_at":"2026-07-15T08:56:53Z","title":"Equilibrium stability as a driver of cooperation among Q-learners"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13607","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":"sha256:02f6d5aded722fc87191f1850d16c31729bec084abb69bb16a5cc51a78dffbac","target":"record","created_at":"2026-07-16T01:22:56Z","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":"c9f51f0283c7476e4dc1ba378fd9ca3b2864c212015c1c75e7d6b4286238c957","cross_cats_sorted":["econ.GN","econ.TH","q-fin.EC"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.MA","submitted_at":"2026-07-15T08:56:53Z","title_canon_sha256":"eaa8378f7a459cbd4cd57dcb815cd4d38add0a7fe849371db70c3087f928a5c9"},"schema_version":"1.0","source":{"id":"2607.13607","kind":"arxiv","version":1}},"canonical_sha256":"192d6766cb879ff13fa19946100a859d74fed6cda5739eb34d748748a70fb42b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"192d6766cb879ff13fa19946100a859d74fed6cda5739eb34d748748a70fb42b","first_computed_at":"2026-07-16T01:22:56.698206Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-16T01:22:56.698206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KvvH7VSl9as6JSWrxGB+ihBwiE1WdSSAnWPNWxTQ7xE4KKDtvoO+McqQm1xGYmh5pC9+P0+vnVnaqvjp5FcSAA==","signature_status":"signed_v1","signed_at":"2026-07-16T01:22:56.699055Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.13607","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02f6d5aded722fc87191f1850d16c31729bec084abb69bb16a5cc51a78dffbac","sha256:96040924bb2523b1619be6afc51edb49ff429b934ea8aa6c09d3969a171c8d1c"],"state_sha256":"dbec92982f5a7a51c3d7c3affdb43a486b37084f562d46c4754b5a08eea794d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2KjOoCPiV9mM0aVDZHkBwqbpXrqWVnTLw9mArd88od9Nq0kYgMmiDQ09utdCT672HNp6Ii94uL0X7kUYXd3rDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T18:22:53.978764Z","bundle_sha256":"f991fac845ae4644315187488e9866a77bfafd35cfc403bd51517b7b1837283e"}}