{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:7HWWZHJLL36BII4CZGX73PJWMT","short_pith_number":"pith:7HWWZHJL","canonical_record":{"source":{"id":"2607.28867","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.AO","submitted_at":"2026-07-30T22:19:32Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"c46d5994794db1504205eefb7f3d0f91c9aeceb2d3e696a2fc0a6b015aa5dfa2","abstract_canon_sha256":"ee099dd8a3375550567478abfc18d5f75dc20fb88a1608a0ef0fe426489c91a2"},"schema_version":"1.0"},"canonical_sha256":"f9ed6c9d2b5efc142382c9affdbd3664d8d78deec10fd1b27defe7276340d54a","source":{"kind":"arxiv","id":"2607.28867","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.28867","created_at":"2026-08-03T01:17:14Z"},{"alias_kind":"arxiv_version","alias_value":"2607.28867v1","created_at":"2026-08-03T01:17:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28867","created_at":"2026-08-03T01:17:14Z"},{"alias_kind":"pith_short_12","alias_value":"7HWWZHJLL36B","created_at":"2026-08-03T01:17:14Z"},{"alias_kind":"pith_short_16","alias_value":"7HWWZHJLL36BII4C","created_at":"2026-08-03T01:17:14Z"},{"alias_kind":"pith_short_8","alias_value":"7HWWZHJL","created_at":"2026-08-03T01:17:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:7HWWZHJLL36BII4CZGX73PJWMT","target":"record","payload":{"canonical_record":{"source":{"id":"2607.28867","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.AO","submitted_at":"2026-07-30T22:19:32Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"c46d5994794db1504205eefb7f3d0f91c9aeceb2d3e696a2fc0a6b015aa5dfa2","abstract_canon_sha256":"ee099dd8a3375550567478abfc18d5f75dc20fb88a1608a0ef0fe426489c91a2"},"schema_version":"1.0"},"canonical_sha256":"f9ed6c9d2b5efc142382c9affdbd3664d8d78deec10fd1b27defe7276340d54a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-03T01:17:14.513732Z","signature_b64":"1u97lb4ugJkJx8yPSNUR15u1AlujSDvUXxGnZaBnVEaGHT6KUBAkhB27w2Qy7zMg9Vvp/us+4tPuA5dcqGFxAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9ed6c9d2b5efc142382c9affdbd3664d8d78deec10fd1b27defe7276340d54a","last_reissued_at":"2026-08-03T01:17:14.512268Z","signature_status":"signed_v1","first_computed_at":"2026-08-03T01:17:14.512268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.28867","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":"2026-08-03T01:17:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uAW8ofkZFkvoyACdWPPPMXfSh+fArsYtMEqpCqg5dhpjFTNP9mHXT74X8omrjX+liL+rY4i5sJITZjWxKNjCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T16:32:46.445200Z"},"content_sha256":"eb2c6c2be39ae0e1420a77a8a96399d9fa000fffafdd374e9922394285fc8e4b","schema_version":"1.0","event_id":"sha256:eb2c6c2be39ae0e1420a77a8a96399d9fa000fffafdd374e9922394285fc8e4b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:7HWWZHJLL36BII4CZGX73PJWMT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Synchrony by Birth and Death","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"nlin.AO","authors_text":"K. P. O'Keeffe","submitted_at":"2026-07-30T22:19:32Z","abstract_excerpt":"A population of oscillators typically synchronizes because coupling pulls their phases together. Here we consider malthusian oscillators whose coupling is demographic: oscillators are born and die at rates determined by their phases, generating an effective coupling without any phase velocity interaction. We find this coupling can synchronize a population, select a collective frequency, and produce a nongeneric fourth-root onset of coherence. These collective dynamics admit an exact reduction: a population with $m$ frequency classes reduces to $3m$ ordinary differential equations. This is the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28867","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/2607.28867/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":"2026-08-03T01:17:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gJ9eirVOdGzbtOS3G9XFECviTWrnwYRbcDOnobjSv9LSK1o9QNSxd0b0dqWJfsr13O13iK8bb33mPdJmA4wLCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T16:32:46.446186Z"},"content_sha256":"4505e158f83fdb7837069963cfb8906d10324ef364077be6832f9cbf1d0ebb77","schema_version":"1.0","event_id":"sha256:4505e158f83fdb7837069963cfb8906d10324ef364077be6832f9cbf1d0ebb77"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7HWWZHJLL36BII4CZGX73PJWMT/bundle.json","state_url":"https://pith.science/pith/7HWWZHJLL36BII4CZGX73PJWMT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7HWWZHJLL36BII4CZGX73PJWMT/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":"2026-08-13T16:32:46Z","links":{"resolver":"https://pith.science/pith/7HWWZHJLL36BII4CZGX73PJWMT","bundle":"https://pith.science/pith/7HWWZHJLL36BII4CZGX73PJWMT/bundle.json","state":"https://pith.science/pith/7HWWZHJLL36BII4CZGX73PJWMT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7HWWZHJLL36BII4CZGX73PJWMT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7HWWZHJLL36BII4CZGX73PJWMT","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":"ee099dd8a3375550567478abfc18d5f75dc20fb88a1608a0ef0fe426489c91a2","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.AO","submitted_at":"2026-07-30T22:19:32Z","title_canon_sha256":"c46d5994794db1504205eefb7f3d0f91c9aeceb2d3e696a2fc0a6b015aa5dfa2"},"schema_version":"1.0","source":{"id":"2607.28867","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.28867","created_at":"2026-08-03T01:17:14Z"},{"alias_kind":"arxiv_version","alias_value":"2607.28867v1","created_at":"2026-08-03T01:17:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28867","created_at":"2026-08-03T01:17:14Z"},{"alias_kind":"pith_short_12","alias_value":"7HWWZHJLL36B","created_at":"2026-08-03T01:17:14Z"},{"alias_kind":"pith_short_16","alias_value":"7HWWZHJLL36BII4C","created_at":"2026-08-03T01:17:14Z"},{"alias_kind":"pith_short_8","alias_value":"7HWWZHJL","created_at":"2026-08-03T01:17:14Z"}],"graph_snapshots":[{"event_id":"sha256:4505e158f83fdb7837069963cfb8906d10324ef364077be6832f9cbf1d0ebb77","target":"graph","created_at":"2026-08-03T01:17:14Z","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/2607.28867/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A population of oscillators typically synchronizes because coupling pulls their phases together. Here we consider malthusian oscillators whose coupling is demographic: oscillators are born and die at rates determined by their phases, generating an effective coupling without any phase velocity interaction. We find this coupling can synchronize a population, select a collective frequency, and produce a nongeneric fourth-root onset of coherence. These collective dynamics admit an exact reduction: a population with $m$ frequency classes reduces to $3m$ ordinary differential equations. This is the ","authors_text":"K. P. O'Keeffe","cross_cats":["math.DS"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.AO","submitted_at":"2026-07-30T22:19:32Z","title":"Synchrony by Birth and Death"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28867","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:eb2c6c2be39ae0e1420a77a8a96399d9fa000fffafdd374e9922394285fc8e4b","target":"record","created_at":"2026-08-03T01:17:14Z","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":"ee099dd8a3375550567478abfc18d5f75dc20fb88a1608a0ef0fe426489c91a2","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.AO","submitted_at":"2026-07-30T22:19:32Z","title_canon_sha256":"c46d5994794db1504205eefb7f3d0f91c9aeceb2d3e696a2fc0a6b015aa5dfa2"},"schema_version":"1.0","source":{"id":"2607.28867","kind":"arxiv","version":1}},"canonical_sha256":"f9ed6c9d2b5efc142382c9affdbd3664d8d78deec10fd1b27defe7276340d54a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9ed6c9d2b5efc142382c9affdbd3664d8d78deec10fd1b27defe7276340d54a","first_computed_at":"2026-08-03T01:17:14.512268Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-03T01:17:14.512268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1u97lb4ugJkJx8yPSNUR15u1AlujSDvUXxGnZaBnVEaGHT6KUBAkhB27w2Qy7zMg9Vvp/us+4tPuA5dcqGFxAQ==","signature_status":"signed_v1","signed_at":"2026-08-03T01:17:14.513732Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.28867","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb2c6c2be39ae0e1420a77a8a96399d9fa000fffafdd374e9922394285fc8e4b","sha256:4505e158f83fdb7837069963cfb8906d10324ef364077be6832f9cbf1d0ebb77"],"state_sha256":"8641c1b0c0adaf54898e698af9ebdc5322966a7c66bf6e36f014660eda14d17f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aXpwTrc7S96p88IKUjoOGEN0LIIzOQo+P+B8Hi99wP/qO5ozVf0AsRQDXs00rwRymVXryqjiFC+eBosogoQdCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T16:32:46.480701Z","bundle_sha256":"610fb5944699508e0ef98869839df543d5187208d9e72100fc70eab7827e5e46"}}