{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:KESNBNN27665GDWHE4AIO3X4FJ","short_pith_number":"pith:KESNBNN2","canonical_record":{"source":{"id":"2507.22857","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-07-30T17:31:57Z","cross_cats_sorted":["cs.LG","math.AP","math.OC"],"title_canon_sha256":"78c551fe90ed1d6121270aa064575e909d66502c8df79e8f65045d4239072cb9","abstract_canon_sha256":"5019cc533b85e2c09e8eda78483f040dcd8ce21d549e6cc3c3ff21eea321dd5a"},"schema_version":"1.0"},"canonical_sha256":"5124d0b5baffbdd30ec72700876efc2a43acce02f358a9f6c63ab62056b37e08","source":{"kind":"arxiv","id":"2507.22857","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.22857","created_at":"2026-07-05T11:45:50Z"},{"alias_kind":"arxiv_version","alias_value":"2507.22857v1","created_at":"2026-07-05T11:45:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.22857","created_at":"2026-07-05T11:45:50Z"},{"alias_kind":"pith_short_12","alias_value":"KESNBNN27665","created_at":"2026-07-05T11:45:50Z"},{"alias_kind":"pith_short_16","alias_value":"KESNBNN27665GDWH","created_at":"2026-07-05T11:45:50Z"},{"alias_kind":"pith_short_8","alias_value":"KESNBNN2","created_at":"2026-07-05T11:45:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:KESNBNN27665GDWHE4AIO3X4FJ","target":"record","payload":{"canonical_record":{"source":{"id":"2507.22857","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-07-30T17:31:57Z","cross_cats_sorted":["cs.LG","math.AP","math.OC"],"title_canon_sha256":"78c551fe90ed1d6121270aa064575e909d66502c8df79e8f65045d4239072cb9","abstract_canon_sha256":"5019cc533b85e2c09e8eda78483f040dcd8ce21d549e6cc3c3ff21eea321dd5a"},"schema_version":"1.0"},"canonical_sha256":"5124d0b5baffbdd30ec72700876efc2a43acce02f358a9f6c63ab62056b37e08","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:45:50.469219Z","signature_b64":"5xEF+XwL+GkUk7KG2qeNYBzdfXncaxDpcT04Zkf9V2v1kHtpXHq+oLd/zT9RVpTyWSzC4J81h+FckcNKhHK3DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5124d0b5baffbdd30ec72700876efc2a43acce02f358a9f6c63ab62056b37e08","last_reissued_at":"2026-07-05T11:45:50.468727Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:45:50.468727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.22857","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":"2026-07-05T11:45:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sLxTpcQVX40qUN6mpE9j0csd6+e/KBql0n3DbXQWZxbE4/flE06uR00hcRANdklj+4AWaRKwdhzuYY1+3MzPAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T08:35:29.719964Z"},"content_sha256":"7f010374fe6c207129cfe5785c6fad9b67a1ae4f63d9d7f1bb0252865d57b2aa","schema_version":"1.0","event_id":"sha256:7f010374fe6c207129cfe5785c6fad9b67a1ae4f63d9d7f1bb0252865d57b2aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:KESNBNN27665GDWHE4AIO3X4FJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Synchronization of mean-field models on the circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.AP","math.OC"],"primary_cat":"math.DS","authors_text":"Andrew Yao, Philippe Rigollet, Yury Polyanskiy","submitted_at":"2025-07-30T17:31:57Z","abstract_excerpt":"This paper considers a mean-field model of $n$ interacting particles whose state space is the unit circle, a generalization of the classical Kuramoto model. Global synchronization is said to occur if after starting from almost any initial state, all particles coalesce to a common point on the circle. We propose a general synchronization criterion in terms of $L_1$-norm of the third derivative of the particle interaction function. As an application we resolve a conjecture for the so-called self-attention dynamics (stylized model of transformers), by showing synchronization for all $\\beta \\ge -0"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.22857","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/2507.22857/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":"2026-07-05T11:45:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4sqvkEKgRbr7fKcfkok5B2Bf8mmwwWBmnebC962w4W3TdTPkBH/z5NC6WLytkFL2T5Au9Uj/mMUqK6HaE5ZvCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T08:35:29.720458Z"},"content_sha256":"2258b9fe116591c156257362d0c6e1ef444afaeaaae8987766dd39d858fd9492","schema_version":"1.0","event_id":"sha256:2258b9fe116591c156257362d0c6e1ef444afaeaaae8987766dd39d858fd9492"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KESNBNN27665GDWHE4AIO3X4FJ/bundle.json","state_url":"https://pith.science/pith/KESNBNN27665GDWHE4AIO3X4FJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KESNBNN27665GDWHE4AIO3X4FJ/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":"2026-08-05T08:35:29Z","links":{"resolver":"https://pith.science/pith/KESNBNN27665GDWHE4AIO3X4FJ","bundle":"https://pith.science/pith/KESNBNN27665GDWHE4AIO3X4FJ/bundle.json","state":"https://pith.science/pith/KESNBNN27665GDWHE4AIO3X4FJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KESNBNN27665GDWHE4AIO3X4FJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:KESNBNN27665GDWHE4AIO3X4FJ","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":"5019cc533b85e2c09e8eda78483f040dcd8ce21d549e6cc3c3ff21eea321dd5a","cross_cats_sorted":["cs.LG","math.AP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-07-30T17:31:57Z","title_canon_sha256":"78c551fe90ed1d6121270aa064575e909d66502c8df79e8f65045d4239072cb9"},"schema_version":"1.0","source":{"id":"2507.22857","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.22857","created_at":"2026-07-05T11:45:50Z"},{"alias_kind":"arxiv_version","alias_value":"2507.22857v1","created_at":"2026-07-05T11:45:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.22857","created_at":"2026-07-05T11:45:50Z"},{"alias_kind":"pith_short_12","alias_value":"KESNBNN27665","created_at":"2026-07-05T11:45:50Z"},{"alias_kind":"pith_short_16","alias_value":"KESNBNN27665GDWH","created_at":"2026-07-05T11:45:50Z"},{"alias_kind":"pith_short_8","alias_value":"KESNBNN2","created_at":"2026-07-05T11:45:50Z"}],"graph_snapshots":[{"event_id":"sha256:2258b9fe116591c156257362d0c6e1ef444afaeaaae8987766dd39d858fd9492","target":"graph","created_at":"2026-07-05T11:45:50Z","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/2507.22857/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper considers a mean-field model of $n$ interacting particles whose state space is the unit circle, a generalization of the classical Kuramoto model. Global synchronization is said to occur if after starting from almost any initial state, all particles coalesce to a common point on the circle. We propose a general synchronization criterion in terms of $L_1$-norm of the third derivative of the particle interaction function. As an application we resolve a conjecture for the so-called self-attention dynamics (stylized model of transformers), by showing synchronization for all $\\beta \\ge -0","authors_text":"Andrew Yao, Philippe Rigollet, Yury Polyanskiy","cross_cats":["cs.LG","math.AP","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-07-30T17:31:57Z","title":"Synchronization of mean-field models on the circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.22857","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":"sha256:7f010374fe6c207129cfe5785c6fad9b67a1ae4f63d9d7f1bb0252865d57b2aa","target":"record","created_at":"2026-07-05T11:45:50Z","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":"5019cc533b85e2c09e8eda78483f040dcd8ce21d549e6cc3c3ff21eea321dd5a","cross_cats_sorted":["cs.LG","math.AP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-07-30T17:31:57Z","title_canon_sha256":"78c551fe90ed1d6121270aa064575e909d66502c8df79e8f65045d4239072cb9"},"schema_version":"1.0","source":{"id":"2507.22857","kind":"arxiv","version":1}},"canonical_sha256":"5124d0b5baffbdd30ec72700876efc2a43acce02f358a9f6c63ab62056b37e08","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5124d0b5baffbdd30ec72700876efc2a43acce02f358a9f6c63ab62056b37e08","first_computed_at":"2026-07-05T11:45:50.468727Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:45:50.468727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5xEF+XwL+GkUk7KG2qeNYBzdfXncaxDpcT04Zkf9V2v1kHtpXHq+oLd/zT9RVpTyWSzC4J81h+FckcNKhHK3DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:45:50.469219Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.22857","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f010374fe6c207129cfe5785c6fad9b67a1ae4f63d9d7f1bb0252865d57b2aa","sha256:2258b9fe116591c156257362d0c6e1ef444afaeaaae8987766dd39d858fd9492"],"state_sha256":"261b0da48247315f25597f8cb7c3e3a1e6baa5ad643ce51580a089aa0d87173a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tic/w68tmph1d35xDXkYARs64OfRjWAxXX8u1kal7Z7P4naX/nWXjqvUpQ7nkzVjGwW1vU7LH6iuEe2ut9fWAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T08:35:29.724080Z","bundle_sha256":"fed43972a29a30a1a53f5391c87838d7d6b15a3fc1fa0e379a10ef466c7bb36a"}}