{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:M4DR6ESRG45ESUUR7MMYV2NIMC","short_pith_number":"pith:M4DR6ESR","canonical_record":{"source":{"id":"1403.0102","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-03-01T16:15:21Z","cross_cats_sorted":["physics.comp-ph","q-bio.NC"],"title_canon_sha256":"6b4d83421127da0a8beaeb2bf03e7760893b74e2c388ec1a5661e84d2d706b49","abstract_canon_sha256":"dbc5b5cd8d902c54fd208e55662e020bc2d66e44b08a4452262ad98ab6c9e565"},"schema_version":"1.0"},"canonical_sha256":"67071f1251373a495291fb198ae9a860b6f217cb2be3cea764c72ac2b6cf32f3","source":{"kind":"arxiv","id":"1403.0102","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0102","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0102v1","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0102","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"pith_short_12","alias_value":"M4DR6ESRG45E","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"M4DR6ESRG45ESUUR","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"M4DR6ESR","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:M4DR6ESRG45ESUUR7MMYV2NIMC","target":"record","payload":{"canonical_record":{"source":{"id":"1403.0102","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-03-01T16:15:21Z","cross_cats_sorted":["physics.comp-ph","q-bio.NC"],"title_canon_sha256":"6b4d83421127da0a8beaeb2bf03e7760893b74e2c388ec1a5661e84d2d706b49","abstract_canon_sha256":"dbc5b5cd8d902c54fd208e55662e020bc2d66e44b08a4452262ad98ab6c9e565"},"schema_version":"1.0"},"canonical_sha256":"67071f1251373a495291fb198ae9a860b6f217cb2be3cea764c72ac2b6cf32f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:25.737477Z","signature_b64":"YeztDkH9sFcNLWFfv2aVmExRzx0Q9v7NvwACAYKj3dszb6sTIfmijkm7QTbFYy6Tzu3tZ65B+DvIJL3/AnxVDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67071f1251373a495291fb198ae9a860b6f217cb2be3cea764c72ac2b6cf32f3","last_reissued_at":"2026-05-18T02:57:25.736516Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:25.736516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.0102","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":"2026-05-18T02:57:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"02RCRxAiGEzEbFf2laljy/ulnc4SJoLLLjr39rg+KucQj1sw1xNaUxcd8E3+mAFoLik6dUFsKct4aL0CL85XBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:19:59.941446Z"},"content_sha256":"a5915136ba9c9485487dde4b546df779c2f4cbbafd6280f021f65c9474984119","schema_version":"1.0","event_id":"sha256:a5915136ba9c9485487dde4b546df779c2f4cbbafd6280f021f65c9474984119"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:M4DR6ESRG45ESUUR7MMYV2NIMC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Synchronization in populations of sparsely connected pulse-coupled oscillators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph","q-bio.NC"],"primary_cat":"nlin.CD","authors_text":"Alexander Rothkegel, Klaus Lehnertz","submitted_at":"2014-03-01T16:15:21Z","abstract_excerpt":"We propose a population model for $\\delta$-pulse-coupled oscillators with sparse connectivity. The model is given as an evolution equation for the phase density which take the form of a partial differential equation with a non-local term. We discuss the existence and stability of stationary solutions and exemplify our approach for integrate-and-fire-like oscillators. While for strong couplings, the firing rate of stationary solutions diverges and solutions disappear, small couplings allow for partially synchronous states which emerge at a supercritical Andronov-Hopf bifurcation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0102","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":""},"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":"2026-05-18T02:57:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jL4ApHBxMkA8yYr7HIXPB9svY3jzFwE5dfjF+qZ2W+wlCoY4uLhWVAFmpQyO9xenBjOWaaurEcSSpo69wcyqBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:19:59.941801Z"},"content_sha256":"e9101c2b366e7177b7b35234ba769ccc156b0e867eb5a27e6977df37dfeb9672","schema_version":"1.0","event_id":"sha256:e9101c2b366e7177b7b35234ba769ccc156b0e867eb5a27e6977df37dfeb9672"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M4DR6ESRG45ESUUR7MMYV2NIMC/bundle.json","state_url":"https://pith.science/pith/M4DR6ESRG45ESUUR7MMYV2NIMC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M4DR6ESRG45ESUUR7MMYV2NIMC/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":"2026-05-30T09:19:59Z","links":{"resolver":"https://pith.science/pith/M4DR6ESRG45ESUUR7MMYV2NIMC","bundle":"https://pith.science/pith/M4DR6ESRG45ESUUR7MMYV2NIMC/bundle.json","state":"https://pith.science/pith/M4DR6ESRG45ESUUR7MMYV2NIMC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M4DR6ESRG45ESUUR7MMYV2NIMC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:M4DR6ESRG45ESUUR7MMYV2NIMC","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":"dbc5b5cd8d902c54fd208e55662e020bc2d66e44b08a4452262ad98ab6c9e565","cross_cats_sorted":["physics.comp-ph","q-bio.NC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-03-01T16:15:21Z","title_canon_sha256":"6b4d83421127da0a8beaeb2bf03e7760893b74e2c388ec1a5661e84d2d706b49"},"schema_version":"1.0","source":{"id":"1403.0102","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0102","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0102v1","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0102","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"pith_short_12","alias_value":"M4DR6ESRG45E","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"M4DR6ESRG45ESUUR","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"M4DR6ESR","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:e9101c2b366e7177b7b35234ba769ccc156b0e867eb5a27e6977df37dfeb9672","target":"graph","created_at":"2026-05-18T02:57:25Z","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"},"paper":{"abstract_excerpt":"We propose a population model for $\\delta$-pulse-coupled oscillators with sparse connectivity. The model is given as an evolution equation for the phase density which take the form of a partial differential equation with a non-local term. We discuss the existence and stability of stationary solutions and exemplify our approach for integrate-and-fire-like oscillators. While for strong couplings, the firing rate of stationary solutions diverges and solutions disappear, small couplings allow for partially synchronous states which emerge at a supercritical Andronov-Hopf bifurcation.","authors_text":"Alexander Rothkegel, Klaus Lehnertz","cross_cats":["physics.comp-ph","q-bio.NC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-03-01T16:15:21Z","title":"Synchronization in populations of sparsely connected pulse-coupled oscillators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0102","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:a5915136ba9c9485487dde4b546df779c2f4cbbafd6280f021f65c9474984119","target":"record","created_at":"2026-05-18T02:57:25Z","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":"dbc5b5cd8d902c54fd208e55662e020bc2d66e44b08a4452262ad98ab6c9e565","cross_cats_sorted":["physics.comp-ph","q-bio.NC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-03-01T16:15:21Z","title_canon_sha256":"6b4d83421127da0a8beaeb2bf03e7760893b74e2c388ec1a5661e84d2d706b49"},"schema_version":"1.0","source":{"id":"1403.0102","kind":"arxiv","version":1}},"canonical_sha256":"67071f1251373a495291fb198ae9a860b6f217cb2be3cea764c72ac2b6cf32f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67071f1251373a495291fb198ae9a860b6f217cb2be3cea764c72ac2b6cf32f3","first_computed_at":"2026-05-18T02:57:25.736516Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:25.736516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YeztDkH9sFcNLWFfv2aVmExRzx0Q9v7NvwACAYKj3dszb6sTIfmijkm7QTbFYy6Tzu3tZ65B+DvIJL3/AnxVDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:25.737477Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.0102","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5915136ba9c9485487dde4b546df779c2f4cbbafd6280f021f65c9474984119","sha256:e9101c2b366e7177b7b35234ba769ccc156b0e867eb5a27e6977df37dfeb9672"],"state_sha256":"46df8286a845d14d8640a1461db65b0f27a99fc122743b715ef643d59a73ca64"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tM7g3Fp66Z1We8YAWd5EA2xupCw8jhI+XENlPreYbqr1Jl1yAIYO/yNFCtrR/cag4nrPzlt8oz1+S93TAxuMCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T09:19:59.943909Z","bundle_sha256":"a0e927ff233df901143041158c4ceab817a8c82025ed2e9d3d9b66ff5384e25d"}}