{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:H3HSG23ROKIIIIVYSVGURRKKYL","short_pith_number":"pith:H3HSG23R","canonical_record":{"source":{"id":"2410.21097","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-10-28T15:02:15Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"94fbc785a1ca84f22a69964534ca0236565a7aa01bacbad0db0d9b1b395111c9","abstract_canon_sha256":"46b9d842794e639e66d4b650e63bd8a02822a97d36565984c07353eb18c2e335"},"schema_version":"1.0"},"canonical_sha256":"3ecf236b7172908422b8954d48c54ac2f06336399b9a5e1f0d52dc662cd5dcc4","source":{"kind":"arxiv","id":"2410.21097","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.21097","created_at":"2026-07-05T11:29:51Z"},{"alias_kind":"arxiv_version","alias_value":"2410.21097v2","created_at":"2026-07-05T11:29:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.21097","created_at":"2026-07-05T11:29:51Z"},{"alias_kind":"pith_short_12","alias_value":"H3HSG23ROKII","created_at":"2026-07-05T11:29:51Z"},{"alias_kind":"pith_short_16","alias_value":"H3HSG23ROKIIIIVY","created_at":"2026-07-05T11:29:51Z"},{"alias_kind":"pith_short_8","alias_value":"H3HSG23R","created_at":"2026-07-05T11:29:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:H3HSG23ROKIIIIVYSVGURRKKYL","target":"record","payload":{"canonical_record":{"source":{"id":"2410.21097","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-10-28T15:02:15Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"94fbc785a1ca84f22a69964534ca0236565a7aa01bacbad0db0d9b1b395111c9","abstract_canon_sha256":"46b9d842794e639e66d4b650e63bd8a02822a97d36565984c07353eb18c2e335"},"schema_version":"1.0"},"canonical_sha256":"3ecf236b7172908422b8954d48c54ac2f06336399b9a5e1f0d52dc662cd5dcc4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:29:51.500289Z","signature_b64":"vKREg1LrEwB8CUlc9D3iSQGB716pzjr6fhFM4pOlKcmSWVnQyWpeYNEHlTZzRF8/XA1kZ47UBz1Ey8QxV3YjBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ecf236b7172908422b8954d48c54ac2f06336399b9a5e1f0d52dc662cd5dcc4","last_reissued_at":"2026-07-05T11:29:51.499795Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:29:51.499795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.21097","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":"2026-07-05T11:29:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nLQZmG5UptgsJOz9fSyh0vQGKfoWsbzg2r/7czVXpTb7SVjFWXZ1uZbzZzjXz4M8xG4C45scmFlgqW0/DDYmDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T08:03:24.977343Z"},"content_sha256":"f84fb2c7e75dc3e14534016b256bd76b2c259ea0d98c296a9130a54be40a5c4e","schema_version":"1.0","event_id":"sha256:f84fb2c7e75dc3e14534016b256bd76b2c259ea0d98c296a9130a54be40a5c4e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:H3HSG23ROKIIIIVYSVGURRKKYL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Competive Spectral Radius of Families of Nonexpansive Mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OC","authors_text":"Lo\\\"ic Marchesini, Marianne Akian, St\\'ephane Gaubert","submitted_at":"2024-10-28T15:02:15Z","abstract_excerpt":"We consider a new class of repeated zero-sum games in which the payoff is the escape rate of a switched dynamical system, where at every stage, the transition is given by a nonexpansive operator depending on the actions of both players. This generalizes to the two-player (and non-linear) case the notion of joint spectral radius of a family of matrices. We show that the value of this game does exist, and we characterize it in terms of an infinite dimensional non-linear eigenproblem. This provides a two-player analogue of Ma\\~ne's lemma from ergodic control. This also extends to the two-player c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.21097","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.21097/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":"2026-07-05T11:29:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sNnbSVY2uG7XpFdVp3S/Tc9Vlq8/fDni/Kw79gay9WA0ut3GCFhQo/L3xEiHtQEtCB+3toDe/scnrTruTHWCBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T08:03:24.977839Z"},"content_sha256":"7b889ec9ed32506177e2225f44665239856f908f6a29d7675534b9e42e7cbfc5","schema_version":"1.0","event_id":"sha256:7b889ec9ed32506177e2225f44665239856f908f6a29d7675534b9e42e7cbfc5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H3HSG23ROKIIIIVYSVGURRKKYL/bundle.json","state_url":"https://pith.science/pith/H3HSG23ROKIIIIVYSVGURRKKYL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H3HSG23ROKIIIIVYSVGURRKKYL/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":"2026-08-08T08:03:24Z","links":{"resolver":"https://pith.science/pith/H3HSG23ROKIIIIVYSVGURRKKYL","bundle":"https://pith.science/pith/H3HSG23ROKIIIIVYSVGURRKKYL/bundle.json","state":"https://pith.science/pith/H3HSG23ROKIIIIVYSVGURRKKYL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H3HSG23ROKIIIIVYSVGURRKKYL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:H3HSG23ROKIIIIVYSVGURRKKYL","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":"46b9d842794e639e66d4b650e63bd8a02822a97d36565984c07353eb18c2e335","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-10-28T15:02:15Z","title_canon_sha256":"94fbc785a1ca84f22a69964534ca0236565a7aa01bacbad0db0d9b1b395111c9"},"schema_version":"1.0","source":{"id":"2410.21097","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.21097","created_at":"2026-07-05T11:29:51Z"},{"alias_kind":"arxiv_version","alias_value":"2410.21097v2","created_at":"2026-07-05T11:29:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.21097","created_at":"2026-07-05T11:29:51Z"},{"alias_kind":"pith_short_12","alias_value":"H3HSG23ROKII","created_at":"2026-07-05T11:29:51Z"},{"alias_kind":"pith_short_16","alias_value":"H3HSG23ROKIIIIVY","created_at":"2026-07-05T11:29:51Z"},{"alias_kind":"pith_short_8","alias_value":"H3HSG23R","created_at":"2026-07-05T11:29:51Z"}],"graph_snapshots":[{"event_id":"sha256:7b889ec9ed32506177e2225f44665239856f908f6a29d7675534b9e42e7cbfc5","target":"graph","created_at":"2026-07-05T11:29:51Z","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/2410.21097/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a new class of repeated zero-sum games in which the payoff is the escape rate of a switched dynamical system, where at every stage, the transition is given by a nonexpansive operator depending on the actions of both players. This generalizes to the two-player (and non-linear) case the notion of joint spectral radius of a family of matrices. We show that the value of this game does exist, and we characterize it in terms of an infinite dimensional non-linear eigenproblem. This provides a two-player analogue of Ma\\~ne's lemma from ergodic control. This also extends to the two-player c","authors_text":"Lo\\\"ic Marchesini, Marianne Akian, St\\'ephane Gaubert","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-10-28T15:02:15Z","title":"The Competive Spectral Radius of Families of Nonexpansive Mappings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.21097","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:f84fb2c7e75dc3e14534016b256bd76b2c259ea0d98c296a9130a54be40a5c4e","target":"record","created_at":"2026-07-05T11:29:51Z","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":"46b9d842794e639e66d4b650e63bd8a02822a97d36565984c07353eb18c2e335","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-10-28T15:02:15Z","title_canon_sha256":"94fbc785a1ca84f22a69964534ca0236565a7aa01bacbad0db0d9b1b395111c9"},"schema_version":"1.0","source":{"id":"2410.21097","kind":"arxiv","version":2}},"canonical_sha256":"3ecf236b7172908422b8954d48c54ac2f06336399b9a5e1f0d52dc662cd5dcc4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ecf236b7172908422b8954d48c54ac2f06336399b9a5e1f0d52dc662cd5dcc4","first_computed_at":"2026-07-05T11:29:51.499795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:29:51.499795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vKREg1LrEwB8CUlc9D3iSQGB716pzjr6fhFM4pOlKcmSWVnQyWpeYNEHlTZzRF8/XA1kZ47UBz1Ey8QxV3YjBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:29:51.500289Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.21097","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f84fb2c7e75dc3e14534016b256bd76b2c259ea0d98c296a9130a54be40a5c4e","sha256:7b889ec9ed32506177e2225f44665239856f908f6a29d7675534b9e42e7cbfc5"],"state_sha256":"2227cdea624202cffa3bd4399e6fe07fb7f145e36c42f2efe5d8d52ddaab8559"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qpv7k8/sH7Q3Qy+9mN2ifHQ/PB9kslmyaBgco4wxqiXi5uecuc5DGhieBGT3EIx9jdyMNQwCfpbh45z9EkaqAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T08:03:24.982729Z","bundle_sha256":"8d7e6a9b9af2141148217a68c4a79271ee78a4f3cb58658a76b6330a8d3adbb6"}}