{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:O6FJRLMVIVQGZ6PXMIXNBKIJPH","short_pith_number":"pith:O6FJRLMV","canonical_record":{"source":{"id":"2608.05956","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.MA","submitted_at":"2026-08-06T12:30:27Z","cross_cats_sorted":["cs.SY","eess.SY"],"title_canon_sha256":"381c085cc99ebfb9920fbae127891a0e8c467cd5a0e6674a3c11efc720f921c5","abstract_canon_sha256":"6a10e3a55d00d2f3dfd1cef246a905a9939ce42fa74a9e4b52b088e772a70eae"},"schema_version":"1.0"},"canonical_sha256":"778a98ad9545606cf9f7622ed0a90979ea903cabddd01c881f3e51d7c026bfff","source":{"kind":"arxiv","id":"2608.05956","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.05956","created_at":"2026-08-07T00:54:09Z"},{"alias_kind":"arxiv_version","alias_value":"2608.05956v1","created_at":"2026-08-07T00:54:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.05956","created_at":"2026-08-07T00:54:09Z"},{"alias_kind":"pith_short_12","alias_value":"O6FJRLMVIVQG","created_at":"2026-08-07T00:54:09Z"},{"alias_kind":"pith_short_16","alias_value":"O6FJRLMVIVQGZ6PX","created_at":"2026-08-07T00:54:09Z"},{"alias_kind":"pith_short_8","alias_value":"O6FJRLMV","created_at":"2026-08-07T00:54:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:O6FJRLMVIVQGZ6PXMIXNBKIJPH","target":"record","payload":{"canonical_record":{"source":{"id":"2608.05956","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.MA","submitted_at":"2026-08-06T12:30:27Z","cross_cats_sorted":["cs.SY","eess.SY"],"title_canon_sha256":"381c085cc99ebfb9920fbae127891a0e8c467cd5a0e6674a3c11efc720f921c5","abstract_canon_sha256":"6a10e3a55d00d2f3dfd1cef246a905a9939ce42fa74a9e4b52b088e772a70eae"},"schema_version":"1.0"},"canonical_sha256":"778a98ad9545606cf9f7622ed0a90979ea903cabddd01c881f3e51d7c026bfff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-07T00:54:09.381590Z","signature_b64":"S+CesY733OVfc4RklZeIq+FaG2yMsd5CZ4QKQ4jRQyqgAkf/XG2CZyYV4Ct+aoLx3h2s7fzoWS25c9rkta6/Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"778a98ad9545606cf9f7622ed0a90979ea903cabddd01c881f3e51d7c026bfff","last_reissued_at":"2026-08-07T00:54:09.380066Z","signature_status":"signed_v1","first_computed_at":"2026-08-07T00:54:09.380066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.05956","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":"2026-08-07T00:54:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"86bg2DndasLSON7QqeyFncyvmSnxAjJHULyLstFuOCtbpQT9QPCyzszS3tZVXx/AkZTUOCIEn05SgQicE8j/BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T02:15:11.865415Z"},"content_sha256":"57d20bedd7da2a0c0f75ec409c176e00cdfe05859c61c1cf67fd7582b7087b06","schema_version":"1.0","event_id":"sha256:57d20bedd7da2a0c0f75ec409c176e00cdfe05859c61c1cf67fd7582b7087b06"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:O6FJRLMVIVQGZ6PXMIXNBKIJPH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SY","eess.SY"],"primary_cat":"cs.MA","authors_text":"Indrakshi Dey, Nuzhat Khan","submitted_at":"2026-08-06T12:30:27Z","abstract_excerpt":"Orchestrated collectives of large language model (LLM) agents that debate and vote are an emerging form of computational intelligence: the intelligent behaviour resides in the \\emph{interaction}, not in any single agent. They improve task accuracy, yet remain black boxes at the system level: there is no principled test of convergence, no bound on the rounds needed, and no faithful account of what drove a decision. This paper develops a novel framework based on Koopman operator theory and validates its theoretical guarantees on multi-agent consensus dynamics. Treating the collective as one nonl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.05956","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/2608.05956/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":"2026-08-07T00:54:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZkOma9qYCQ5kF8t+DBgdN75uNqfomv3txzhNwEm2C8mC9qyMkN1pDkyUQNIc8B6UB9wY2kUT+Yya87/mS71zBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T02:15:11.866536Z"},"content_sha256":"00b7e62c555196d22c727197aa7b8b05720822413bda5a4b949414c3515f82da","schema_version":"1.0","event_id":"sha256:00b7e62c555196d22c727197aa7b8b05720822413bda5a4b949414c3515f82da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O6FJRLMVIVQGZ6PXMIXNBKIJPH/bundle.json","state_url":"https://pith.science/pith/O6FJRLMVIVQGZ6PXMIXNBKIJPH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O6FJRLMVIVQGZ6PXMIXNBKIJPH/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":"2026-08-10T02:15:11Z","links":{"resolver":"https://pith.science/pith/O6FJRLMVIVQGZ6PXMIXNBKIJPH","bundle":"https://pith.science/pith/O6FJRLMVIVQGZ6PXMIXNBKIJPH/bundle.json","state":"https://pith.science/pith/O6FJRLMVIVQGZ6PXMIXNBKIJPH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O6FJRLMVIVQGZ6PXMIXNBKIJPH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:O6FJRLMVIVQGZ6PXMIXNBKIJPH","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":"6a10e3a55d00d2f3dfd1cef246a905a9939ce42fa74a9e4b52b088e772a70eae","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.MA","submitted_at":"2026-08-06T12:30:27Z","title_canon_sha256":"381c085cc99ebfb9920fbae127891a0e8c467cd5a0e6674a3c11efc720f921c5"},"schema_version":"1.0","source":{"id":"2608.05956","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.05956","created_at":"2026-08-07T00:54:09Z"},{"alias_kind":"arxiv_version","alias_value":"2608.05956v1","created_at":"2026-08-07T00:54:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.05956","created_at":"2026-08-07T00:54:09Z"},{"alias_kind":"pith_short_12","alias_value":"O6FJRLMVIVQG","created_at":"2026-08-07T00:54:09Z"},{"alias_kind":"pith_short_16","alias_value":"O6FJRLMVIVQGZ6PX","created_at":"2026-08-07T00:54:09Z"},{"alias_kind":"pith_short_8","alias_value":"O6FJRLMV","created_at":"2026-08-07T00:54:09Z"}],"graph_snapshots":[{"event_id":"sha256:00b7e62c555196d22c727197aa7b8b05720822413bda5a4b949414c3515f82da","target":"graph","created_at":"2026-08-07T00:54:09Z","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/2608.05956/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Orchestrated collectives of large language model (LLM) agents that debate and vote are an emerging form of computational intelligence: the intelligent behaviour resides in the \\emph{interaction}, not in any single agent. They improve task accuracy, yet remain black boxes at the system level: there is no principled test of convergence, no bound on the rounds needed, and no faithful account of what drove a decision. This paper develops a novel framework based on Koopman operator theory and validates its theoretical guarantees on multi-agent consensus dynamics. Treating the collective as one nonl","authors_text":"Indrakshi Dey, Nuzhat Khan","cross_cats":["cs.SY","eess.SY"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.MA","submitted_at":"2026-08-06T12:30:27Z","title":"Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.05956","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":"sha256:57d20bedd7da2a0c0f75ec409c176e00cdfe05859c61c1cf67fd7582b7087b06","target":"record","created_at":"2026-08-07T00:54:09Z","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":"6a10e3a55d00d2f3dfd1cef246a905a9939ce42fa74a9e4b52b088e772a70eae","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.MA","submitted_at":"2026-08-06T12:30:27Z","title_canon_sha256":"381c085cc99ebfb9920fbae127891a0e8c467cd5a0e6674a3c11efc720f921c5"},"schema_version":"1.0","source":{"id":"2608.05956","kind":"arxiv","version":1}},"canonical_sha256":"778a98ad9545606cf9f7622ed0a90979ea903cabddd01c881f3e51d7c026bfff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"778a98ad9545606cf9f7622ed0a90979ea903cabddd01c881f3e51d7c026bfff","first_computed_at":"2026-08-07T00:54:09.380066Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-07T00:54:09.380066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S+CesY733OVfc4RklZeIq+FaG2yMsd5CZ4QKQ4jRQyqgAkf/XG2CZyYV4Ct+aoLx3h2s7fzoWS25c9rkta6/Bg==","signature_status":"signed_v1","signed_at":"2026-08-07T00:54:09.381590Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.05956","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57d20bedd7da2a0c0f75ec409c176e00cdfe05859c61c1cf67fd7582b7087b06","sha256:00b7e62c555196d22c727197aa7b8b05720822413bda5a4b949414c3515f82da"],"state_sha256":"d4b65d5ee8b405ce4b8059cf13cd7587ab790b42331cb7760c1ebc1bd6f0a28a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I4vqJsUUyA9Tl6cH5RUwptNgc2x8WQjnot4oKYELJgVk+tI8Y41I6klMOfF7lxX8fPu+f3yr7zdb2Xh5zHvmCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T02:15:11.873617Z","bundle_sha256":"1861d199f749d67e7eb9bf5d352af28df25c5b5312eaf62c86ad933cd6671ea6"}}