{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:YMPDJVDIAB3BMOZXDU4YL3J44E","short_pith_number":"pith:YMPDJVDI","canonical_record":{"source":{"id":"0910.0627","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-10-04T19:31:06Z","cross_cats_sorted":["cond-mat.dis-nn","q-bio.NC"],"title_canon_sha256":"45f644d6d108fc65b5b383bb009a61224df59c6c0eb50905830653acd1bbd455","abstract_canon_sha256":"0ae773fb334b9b0a4c448f1e30bf625bab9f2ad10e96de25e3088a6ef689597e"},"schema_version":"1.0"},"canonical_sha256":"c31e34d4680076163b371d3985ed3ce133aec5d2deba073da7ea8cf544d783d6","source":{"kind":"arxiv","id":"0910.0627","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.0627","created_at":"2026-05-18T02:11:26Z"},{"alias_kind":"arxiv_version","alias_value":"0910.0627v1","created_at":"2026-05-18T02:11:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.0627","created_at":"2026-05-18T02:11:26Z"},{"alias_kind":"pith_short_12","alias_value":"YMPDJVDIAB3B","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YMPDJVDIAB3BMOZX","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YMPDJVDI","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:YMPDJVDIAB3BMOZXDU4YL3J44E","target":"record","payload":{"canonical_record":{"source":{"id":"0910.0627","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-10-04T19:31:06Z","cross_cats_sorted":["cond-mat.dis-nn","q-bio.NC"],"title_canon_sha256":"45f644d6d108fc65b5b383bb009a61224df59c6c0eb50905830653acd1bbd455","abstract_canon_sha256":"0ae773fb334b9b0a4c448f1e30bf625bab9f2ad10e96de25e3088a6ef689597e"},"schema_version":"1.0"},"canonical_sha256":"c31e34d4680076163b371d3985ed3ce133aec5d2deba073da7ea8cf544d783d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:11:26.869048Z","signature_b64":"/7TNOtHPScYvBipjGdj6qnldzbc3M3gtwiwBsNFt6Kr4Ly4M7gFAA+6ONJ9sqUjCAb9WDhk+DHY1HfdupUwhBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c31e34d4680076163b371d3985ed3ce133aec5d2deba073da7ea8cf544d783d6","last_reissued_at":"2026-05-18T02:11:26.868195Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:11:26.868195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0910.0627","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":"2026-05-18T02:11:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vXVYeE8D7iCDx4sGX+1e9k/HzrsYTqEBQCQ77n28zodEuxQYG2VWPFNuDJ2LrDZDFoqNWRM2vsacpp5L/8jLAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:17:36.359431Z"},"content_sha256":"878c8624e25ab029b1ba1e9bc83fa7e8d327c3a1f2ade03d173f389de7a9d65c","schema_version":"1.0","event_id":"sha256:878c8624e25ab029b1ba1e9bc83fa7e8d327c3a1f2ade03d173f389de7a9d65c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:YMPDJVDIAB3BMOZXDU4YL3J44E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Bootstrap Percolation in Living Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","q-bio.NC"],"primary_cat":"math.PR","authors_text":"Hamed Amini","submitted_at":"2009-10-04T19:31:06Z","abstract_excerpt":"Recent experimental studies of living neural networks reveal that their global activation induced by electrical stimulation can be explained using the concept of bootstrap percolation on a directed random network. The experiment consists in activating externally an initial random fraction of the neurons and observe the process of firing until its equilibrium. The final portion of neurons that are active depends in a non linear way on the initial fraction. The main result of this paper is a theorem which enables us to find the asymptotic of final proportion of the fired neurons in the case of r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.0627","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":"2026-05-18T02:11:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y/+HFlozwmzSZvC8MPdLfcQTbguyV4ivMQyzvC1WqhyxTxQqi4uj78ZVN8RyQTybKlhYoUXCNiGEzYGQMla4Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:17:36.359769Z"},"content_sha256":"c3d4a44de6e0b4238547e417020618152d8e93fd9e5b24dc09c89e207a24b04c","schema_version":"1.0","event_id":"sha256:c3d4a44de6e0b4238547e417020618152d8e93fd9e5b24dc09c89e207a24b04c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YMPDJVDIAB3BMOZXDU4YL3J44E/bundle.json","state_url":"https://pith.science/pith/YMPDJVDIAB3BMOZXDU4YL3J44E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YMPDJVDIAB3BMOZXDU4YL3J44E/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":"2026-06-25T08:17:36Z","links":{"resolver":"https://pith.science/pith/YMPDJVDIAB3BMOZXDU4YL3J44E","bundle":"https://pith.science/pith/YMPDJVDIAB3BMOZXDU4YL3J44E/bundle.json","state":"https://pith.science/pith/YMPDJVDIAB3BMOZXDU4YL3J44E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YMPDJVDIAB3BMOZXDU4YL3J44E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:YMPDJVDIAB3BMOZXDU4YL3J44E","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":"0ae773fb334b9b0a4c448f1e30bf625bab9f2ad10e96de25e3088a6ef689597e","cross_cats_sorted":["cond-mat.dis-nn","q-bio.NC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-10-04T19:31:06Z","title_canon_sha256":"45f644d6d108fc65b5b383bb009a61224df59c6c0eb50905830653acd1bbd455"},"schema_version":"1.0","source":{"id":"0910.0627","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.0627","created_at":"2026-05-18T02:11:26Z"},{"alias_kind":"arxiv_version","alias_value":"0910.0627v1","created_at":"2026-05-18T02:11:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.0627","created_at":"2026-05-18T02:11:26Z"},{"alias_kind":"pith_short_12","alias_value":"YMPDJVDIAB3B","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YMPDJVDIAB3BMOZX","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YMPDJVDI","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:c3d4a44de6e0b4238547e417020618152d8e93fd9e5b24dc09c89e207a24b04c","target":"graph","created_at":"2026-05-18T02:11:26Z","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":"Recent experimental studies of living neural networks reveal that their global activation induced by electrical stimulation can be explained using the concept of bootstrap percolation on a directed random network. The experiment consists in activating externally an initial random fraction of the neurons and observe the process of firing until its equilibrium. The final portion of neurons that are active depends in a non linear way on the initial fraction. The main result of this paper is a theorem which enables us to find the asymptotic of final proportion of the fired neurons in the case of r","authors_text":"Hamed Amini","cross_cats":["cond-mat.dis-nn","q-bio.NC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-10-04T19:31:06Z","title":"On Bootstrap Percolation in Living Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.0627","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":"sha256:878c8624e25ab029b1ba1e9bc83fa7e8d327c3a1f2ade03d173f389de7a9d65c","target":"record","created_at":"2026-05-18T02:11:26Z","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":"0ae773fb334b9b0a4c448f1e30bf625bab9f2ad10e96de25e3088a6ef689597e","cross_cats_sorted":["cond-mat.dis-nn","q-bio.NC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-10-04T19:31:06Z","title_canon_sha256":"45f644d6d108fc65b5b383bb009a61224df59c6c0eb50905830653acd1bbd455"},"schema_version":"1.0","source":{"id":"0910.0627","kind":"arxiv","version":1}},"canonical_sha256":"c31e34d4680076163b371d3985ed3ce133aec5d2deba073da7ea8cf544d783d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c31e34d4680076163b371d3985ed3ce133aec5d2deba073da7ea8cf544d783d6","first_computed_at":"2026-05-18T02:11:26.868195Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:11:26.868195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/7TNOtHPScYvBipjGdj6qnldzbc3M3gtwiwBsNFt6Kr4Ly4M7gFAA+6ONJ9sqUjCAb9WDhk+DHY1HfdupUwhBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:11:26.869048Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.0627","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:878c8624e25ab029b1ba1e9bc83fa7e8d327c3a1f2ade03d173f389de7a9d65c","sha256:c3d4a44de6e0b4238547e417020618152d8e93fd9e5b24dc09c89e207a24b04c"],"state_sha256":"c1eeb757f8214bdae0334773d36ec73b5cc717a2f38a480297b239454616a6dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D0twmLrJvJe1F6UihogsVT4ampBmlZH4dsZ+tLbkUzbOpCciIwmes3a0RgBboZ2NheG/35h7+weuWlj9rnDDCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T08:17:36.361634Z","bundle_sha256":"b0ec53e44c2bc5b2be8a2f9063483578de6095d0eb60e453ef47f3cc1a1631f9"}}