{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:5JBBCI2BFG5ULTXBINNLTME4JQ","short_pith_number":"pith:5JBBCI2B","canonical_record":{"source":{"id":"1002.3798","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-02-19T18:57:47Z","cross_cats_sorted":["q-bio.NC","stat.ME"],"title_canon_sha256":"024f6b90878e488cd0deaf7667d7d76f61f647045d105115ce0ef8232068b8a9","abstract_canon_sha256":"857b5770788430bdc276d7b81dd5ad5263109994660716185280893f024f1c0a"},"schema_version":"1.0"},"canonical_sha256":"ea4211234129bb45cee1435ab9b09c4c3cd5b0490c2b0636a6bca0c6efadd0dd","source":{"kind":"arxiv","id":"1002.3798","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.3798","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"arxiv_version","alias_value":"1002.3798v3","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.3798","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"pith_short_12","alias_value":"5JBBCI2BFG5U","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5JBBCI2BFG5ULTXB","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5JBBCI2B","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:5JBBCI2BFG5ULTXBINNLTME4JQ","target":"record","payload":{"canonical_record":{"source":{"id":"1002.3798","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-02-19T18:57:47Z","cross_cats_sorted":["q-bio.NC","stat.ME"],"title_canon_sha256":"024f6b90878e488cd0deaf7667d7d76f61f647045d105115ce0ef8232068b8a9","abstract_canon_sha256":"857b5770788430bdc276d7b81dd5ad5263109994660716185280893f024f1c0a"},"schema_version":"1.0"},"canonical_sha256":"ea4211234129bb45cee1435ab9b09c4c3cd5b0490c2b0636a6bca0c6efadd0dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:21.359370Z","signature_b64":"Ns8dNNuMXwTXMKqsnC3JMEKo7FRa0ub+SMezjZ4HJPZvDos40eZU3JcaG+Ww3DnvO1jp53rOpf2AdGQFTlFUCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea4211234129bb45cee1435ab9b09c4c3cd5b0490c2b0636a6bca0c6efadd0dd","last_reissued_at":"2026-05-18T01:36:21.358752Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:21.358752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.3798","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:36:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aJDodGUrpiyWalchmOQFPEdU11gKRQP4kvD8FsV0sUMOSH7Zvx4Y4He/17PS20nyKBxXXP+ybsOVC9w4b+MNAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T14:47:46.193717Z"},"content_sha256":"5f5efc155eeb3414a73093eadfd5cec15b5e174da5038c0ef02c10d5a60d60ea","schema_version":"1.0","event_id":"sha256:5f5efc155eeb3414a73093eadfd5cec15b5e174da5038c0ef02c10d5a60d60ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:5JBBCI2BFG5ULTXBINNLTME4JQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-equilibrium dynamics of stochastic point processes with refractoriness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.NC","stat.ME"],"primary_cat":"math.PR","authors_text":"Fatihcan M. Atay, Moritz Deger, Moritz Helias, Stefano Cardanobile, Stefan Rotter","submitted_at":"2010-02-19T18:57:47Z","abstract_excerpt":"Stochastic point processes with refractoriness appear frequently in the quantitative analysis of physical and biological systems, such as the generation of action potentials by nerve cells, the release and reuptake of vesicles at a synapse, and the counting of particles by detector devices. Here we present an extension of renewal theory to describe ensembles of point processes with time varying input. This is made possible by a representation in terms of occupation numbers of two states: Active and refractory. The dynamics of these occupation numbers follows a distributed delay differential eq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3798","kind":"arxiv","version":3},"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":"2026-05-18T01:36:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b1OfsTIH9YDtojxOnwm692wuCIw99iTGE68mGmHyMGHOVBELCd71bExH10S5TD2fGaranP784+V/umSwXATjAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T14:47:46.194047Z"},"content_sha256":"df6280bbf1d073b78edeac7a0057fde3b11df51e139f2633e11abbf5afea9763","schema_version":"1.0","event_id":"sha256:df6280bbf1d073b78edeac7a0057fde3b11df51e139f2633e11abbf5afea9763"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5JBBCI2BFG5ULTXBINNLTME4JQ/bundle.json","state_url":"https://pith.science/pith/5JBBCI2BFG5ULTXBINNLTME4JQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5JBBCI2BFG5ULTXBINNLTME4JQ/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":"2026-06-20T14:47:46Z","links":{"resolver":"https://pith.science/pith/5JBBCI2BFG5ULTXBINNLTME4JQ","bundle":"https://pith.science/pith/5JBBCI2BFG5ULTXBINNLTME4JQ/bundle.json","state":"https://pith.science/pith/5JBBCI2BFG5ULTXBINNLTME4JQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5JBBCI2BFG5ULTXBINNLTME4JQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5JBBCI2BFG5ULTXBINNLTME4JQ","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":"857b5770788430bdc276d7b81dd5ad5263109994660716185280893f024f1c0a","cross_cats_sorted":["q-bio.NC","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-02-19T18:57:47Z","title_canon_sha256":"024f6b90878e488cd0deaf7667d7d76f61f647045d105115ce0ef8232068b8a9"},"schema_version":"1.0","source":{"id":"1002.3798","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.3798","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"arxiv_version","alias_value":"1002.3798v3","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.3798","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"pith_short_12","alias_value":"5JBBCI2BFG5U","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5JBBCI2BFG5ULTXB","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5JBBCI2B","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:df6280bbf1d073b78edeac7a0057fde3b11df51e139f2633e11abbf5afea9763","target":"graph","created_at":"2026-05-18T01:36:21Z","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":"Stochastic point processes with refractoriness appear frequently in the quantitative analysis of physical and biological systems, such as the generation of action potentials by nerve cells, the release and reuptake of vesicles at a synapse, and the counting of particles by detector devices. Here we present an extension of renewal theory to describe ensembles of point processes with time varying input. This is made possible by a representation in terms of occupation numbers of two states: Active and refractory. The dynamics of these occupation numbers follows a distributed delay differential eq","authors_text":"Fatihcan M. Atay, Moritz Deger, Moritz Helias, Stefano Cardanobile, Stefan Rotter","cross_cats":["q-bio.NC","stat.ME"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-02-19T18:57:47Z","title":"Non-equilibrium dynamics of stochastic point processes with refractoriness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3798","kind":"arxiv","version":3},"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":"sha256:5f5efc155eeb3414a73093eadfd5cec15b5e174da5038c0ef02c10d5a60d60ea","target":"record","created_at":"2026-05-18T01:36:21Z","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":"857b5770788430bdc276d7b81dd5ad5263109994660716185280893f024f1c0a","cross_cats_sorted":["q-bio.NC","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-02-19T18:57:47Z","title_canon_sha256":"024f6b90878e488cd0deaf7667d7d76f61f647045d105115ce0ef8232068b8a9"},"schema_version":"1.0","source":{"id":"1002.3798","kind":"arxiv","version":3}},"canonical_sha256":"ea4211234129bb45cee1435ab9b09c4c3cd5b0490c2b0636a6bca0c6efadd0dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea4211234129bb45cee1435ab9b09c4c3cd5b0490c2b0636a6bca0c6efadd0dd","first_computed_at":"2026-05-18T01:36:21.358752Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:21.358752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ns8dNNuMXwTXMKqsnC3JMEKo7FRa0ub+SMezjZ4HJPZvDos40eZU3JcaG+Ww3DnvO1jp53rOpf2AdGQFTlFUCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:21.359370Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.3798","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f5efc155eeb3414a73093eadfd5cec15b5e174da5038c0ef02c10d5a60d60ea","sha256:df6280bbf1d073b78edeac7a0057fde3b11df51e139f2633e11abbf5afea9763"],"state_sha256":"763b1f3a260f5578896694dd84548f662165e37cd95172b959fad73d2c7e6d80"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WjaBFh67NqOKs+x9FowtCQWS5MYZ9x7TIvR6c4fCOEm32pK43mYwURHafkz4wSdJ0qPqOrQ43XrUwSaA8MOQAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T14:47:46.195916Z","bundle_sha256":"e9f8025d77856476433d3a448cdd19cc68a19408e4edfa13cb956182b2f496a3"}}