{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:NMRQQM5KTW5QN4C6ADD6IHZLEB","short_pith_number":"pith:NMRQQM5K","canonical_record":{"source":{"id":"2505.21088","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2025-05-27T12:15:38Z","cross_cats_sorted":[],"title_canon_sha256":"56fbf2978d3d7b94e71ab41e8abae7b6747874956adf118547276d5be1cf9dac","abstract_canon_sha256":"ca70ae35eae395479f4f23e96763a431f365c2f1378101d2282cb1125d30e50c"},"schema_version":"1.0"},"canonical_sha256":"6b230833aa9dbb06f05e00c7e41f2b207dbbfdf19bad69ce5fd58cd6217d0d18","source":{"kind":"arxiv","id":"2505.21088","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.21088","created_at":"2026-07-05T11:10:23Z"},{"alias_kind":"arxiv_version","alias_value":"2505.21088v1","created_at":"2026-07-05T11:10:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21088","created_at":"2026-07-05T11:10:23Z"},{"alias_kind":"pith_short_12","alias_value":"NMRQQM5KTW5Q","created_at":"2026-07-05T11:10:23Z"},{"alias_kind":"pith_short_16","alias_value":"NMRQQM5KTW5QN4C6","created_at":"2026-07-05T11:10:23Z"},{"alias_kind":"pith_short_8","alias_value":"NMRQQM5K","created_at":"2026-07-05T11:10:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:NMRQQM5KTW5QN4C6ADD6IHZLEB","target":"record","payload":{"canonical_record":{"source":{"id":"2505.21088","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2025-05-27T12:15:38Z","cross_cats_sorted":[],"title_canon_sha256":"56fbf2978d3d7b94e71ab41e8abae7b6747874956adf118547276d5be1cf9dac","abstract_canon_sha256":"ca70ae35eae395479f4f23e96763a431f365c2f1378101d2282cb1125d30e50c"},"schema_version":"1.0"},"canonical_sha256":"6b230833aa9dbb06f05e00c7e41f2b207dbbfdf19bad69ce5fd58cd6217d0d18","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:10:23.482980Z","signature_b64":"8TA12m/4fhtZJ96ygSZpynJfdenwd9Dz1FRuSAI1k3KHsEggJH8DHWs6Ptnss7hgFVu/67qM0/HShpdyk1RSDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b230833aa9dbb06f05e00c7e41f2b207dbbfdf19bad69ce5fd58cd6217d0d18","last_reissued_at":"2026-07-05T11:10:23.482493Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:10:23.482493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.21088","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":"2026-07-05T11:10:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bf0vrLT2Spb2IJSSbaRMm+hcGYRnESrX6LvNHsRMZwozFLJuGUNMquKN/KZbwf0fFaVisWU7ykbCJBqXupXNCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T01:57:21.176252Z"},"content_sha256":"8360ebf30d8a29f3a698281368a06a169998b3258e49650960fa59f434d2b853","schema_version":"1.0","event_id":"sha256:8360ebf30d8a29f3a698281368a06a169998b3258e49650960fa59f434d2b853"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:NMRQQM5KTW5QN4C6ADD6IHZLEB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Synchronization Phenomenon in Three-Time-Scale Systems","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Navojit Dhali Pallab","submitted_at":"2025-05-27T12:15:38Z","abstract_excerpt":"This paper investigates synchronization phenomena in networks of coupled oscillators governed by three-time-scale dynamical systems exhibiting canard dynamics. A mathematical framework has been developed to analyze the synchronization of fast variables across heterogeneous systems, deriving a sufficient condition for the synchronization error to fall below a specified threshold within the minimum linger time. This condition accounts for coupling strength, heterogeneity, and time-scale separation, ensuring stable oscillatory behavior in the network. The result, supported by rigorous mathematica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21088","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/2505.21088/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":"2026-07-05T11:10:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gOcDy+32t+4N+LeTwveN+pnniGbA/0exVi1fwfqt2t81MO+hY/KE1Uzy+QATPNm23i4+bZyxGAMqwT0V2bY7AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T01:57:21.176860Z"},"content_sha256":"2b912438986f7a4a69305b0f8d14d6477f4f1dc29319fa769fd5dc9a2b4399dc","schema_version":"1.0","event_id":"sha256:2b912438986f7a4a69305b0f8d14d6477f4f1dc29319fa769fd5dc9a2b4399dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NMRQQM5KTW5QN4C6ADD6IHZLEB/bundle.json","state_url":"https://pith.science/pith/NMRQQM5KTW5QN4C6ADD6IHZLEB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NMRQQM5KTW5QN4C6ADD6IHZLEB/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":"2026-08-11T01:57:21Z","links":{"resolver":"https://pith.science/pith/NMRQQM5KTW5QN4C6ADD6IHZLEB","bundle":"https://pith.science/pith/NMRQQM5KTW5QN4C6ADD6IHZLEB/bundle.json","state":"https://pith.science/pith/NMRQQM5KTW5QN4C6ADD6IHZLEB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NMRQQM5KTW5QN4C6ADD6IHZLEB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:NMRQQM5KTW5QN4C6ADD6IHZLEB","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":"ca70ae35eae395479f4f23e96763a431f365c2f1378101d2282cb1125d30e50c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2025-05-27T12:15:38Z","title_canon_sha256":"56fbf2978d3d7b94e71ab41e8abae7b6747874956adf118547276d5be1cf9dac"},"schema_version":"1.0","source":{"id":"2505.21088","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.21088","created_at":"2026-07-05T11:10:23Z"},{"alias_kind":"arxiv_version","alias_value":"2505.21088v1","created_at":"2026-07-05T11:10:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21088","created_at":"2026-07-05T11:10:23Z"},{"alias_kind":"pith_short_12","alias_value":"NMRQQM5KTW5Q","created_at":"2026-07-05T11:10:23Z"},{"alias_kind":"pith_short_16","alias_value":"NMRQQM5KTW5QN4C6","created_at":"2026-07-05T11:10:23Z"},{"alias_kind":"pith_short_8","alias_value":"NMRQQM5K","created_at":"2026-07-05T11:10:23Z"}],"graph_snapshots":[{"event_id":"sha256:2b912438986f7a4a69305b0f8d14d6477f4f1dc29319fa769fd5dc9a2b4399dc","target":"graph","created_at":"2026-07-05T11:10:23Z","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/2505.21088/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper investigates synchronization phenomena in networks of coupled oscillators governed by three-time-scale dynamical systems exhibiting canard dynamics. A mathematical framework has been developed to analyze the synchronization of fast variables across heterogeneous systems, deriving a sufficient condition for the synchronization error to fall below a specified threshold within the minimum linger time. This condition accounts for coupling strength, heterogeneity, and time-scale separation, ensuring stable oscillatory behavior in the network. The result, supported by rigorous mathematica","authors_text":"Navojit Dhali Pallab","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2025-05-27T12:15:38Z","title":"Synchronization Phenomenon in Three-Time-Scale Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21088","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":"sha256:8360ebf30d8a29f3a698281368a06a169998b3258e49650960fa59f434d2b853","target":"record","created_at":"2026-07-05T11:10:23Z","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":"ca70ae35eae395479f4f23e96763a431f365c2f1378101d2282cb1125d30e50c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2025-05-27T12:15:38Z","title_canon_sha256":"56fbf2978d3d7b94e71ab41e8abae7b6747874956adf118547276d5be1cf9dac"},"schema_version":"1.0","source":{"id":"2505.21088","kind":"arxiv","version":1}},"canonical_sha256":"6b230833aa9dbb06f05e00c7e41f2b207dbbfdf19bad69ce5fd58cd6217d0d18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b230833aa9dbb06f05e00c7e41f2b207dbbfdf19bad69ce5fd58cd6217d0d18","first_computed_at":"2026-07-05T11:10:23.482493Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:10:23.482493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8TA12m/4fhtZJ96ygSZpynJfdenwd9Dz1FRuSAI1k3KHsEggJH8DHWs6Ptnss7hgFVu/67qM0/HShpdyk1RSDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:10:23.482980Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.21088","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8360ebf30d8a29f3a698281368a06a169998b3258e49650960fa59f434d2b853","sha256:2b912438986f7a4a69305b0f8d14d6477f4f1dc29319fa769fd5dc9a2b4399dc"],"state_sha256":"4c49b43b9ae86100583a768a1759300a99e4092fc5b63ce619f3d71355f05381"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YP0PCjmuBVB9MlqfV1MRGlKcWZX7bsU0xklQiszkM5OTwpKVZnjyUrwmFhRn86pQ9+SCUjYPKaucwE/H4TidAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T01:57:21.180415Z","bundle_sha256":"a2817d0ec61bf13620e99f87f6b778f4a6c88b05697d4e85577a65878620200b"}}