{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:Q43JDBXESTURZBQFDQ63SWWSFV","short_pith_number":"pith:Q43JDBXE","canonical_record":{"source":{"id":"1810.13198","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2018-10-31T10:24:35Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"63dc6028a09c241b19dee78dbbcf624a94eec36843701ff15e589484c86b9343","abstract_canon_sha256":"7250148ef4e4744a3521b7a086bcca83e423a45d0a00a1a60d8747a6ebf4ed00"},"schema_version":"1.0"},"canonical_sha256":"87369186e494e91c86051c3db95ad22d41f5e78f150fc087fed8ae123049b498","source":{"kind":"arxiv","id":"1810.13198","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.13198","created_at":"2026-05-17T23:49:59Z"},{"alias_kind":"arxiv_version","alias_value":"1810.13198v1","created_at":"2026-05-17T23:49:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.13198","created_at":"2026-05-17T23:49:59Z"},{"alias_kind":"pith_short_12","alias_value":"Q43JDBXESTUR","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"Q43JDBXESTURZBQF","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"Q43JDBXE","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:Q43JDBXESTURZBQFDQ63SWWSFV","target":"record","payload":{"canonical_record":{"source":{"id":"1810.13198","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2018-10-31T10:24:35Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"63dc6028a09c241b19dee78dbbcf624a94eec36843701ff15e589484c86b9343","abstract_canon_sha256":"7250148ef4e4744a3521b7a086bcca83e423a45d0a00a1a60d8747a6ebf4ed00"},"schema_version":"1.0"},"canonical_sha256":"87369186e494e91c86051c3db95ad22d41f5e78f150fc087fed8ae123049b498","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:59.549429Z","signature_b64":"rOMxOMzjzw8hAXHv14LiQgvmzwQXHtgrtemERE+I3TqSMohCYs6mvKSdcnCt93baZb9LoX0MQVUZx0M4gjFTBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87369186e494e91c86051c3db95ad22d41f5e78f150fc087fed8ae123049b498","last_reissued_at":"2026-05-17T23:49:59.549019Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:59.549019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.13198","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":"2026-05-17T23:49:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8KvCCRZVkHUEEFkBz5AY/tcbVEYSGfBpo4xucaWYp/08NCYauChOBi3mFIgC+QuBf7kJIXUvc/8FflzNdmstAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T13:33:20.531785Z"},"content_sha256":"f8a5dbb369c4360d70904b305bca539aba51af8161a15e61eff7940254317b8c","schema_version":"1.0","event_id":"sha256:f8a5dbb369c4360d70904b305bca539aba51af8161a15e61eff7940254317b8c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:Q43JDBXESTURZBQFDQ63SWWSFV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Volterra chain and Catalan numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"nlin.SI","authors_text":"A.B. Shabat, V.E. Adler","submitted_at":"2018-10-31T10:24:35Z","abstract_excerpt":"We consider the Cauchy problem for the Volterra chain with an initial condition equal to 0 in one node and 1 in the others. It is shown that this problem admits an exact solution in terms of the Bessel functions. The Taylor series arising here are related to the exponential generating function for Catalan numbers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.13198","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":"2026-05-17T23:49:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zm6MiFh+OFjRJvnv/1XZ1Oq39myYHGU5oGPevRbFXiw3OhAZapsr0NyfiQW4Yrkobv3Wh5t2UDEqaWDgr0Y4BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T13:33:20.532141Z"},"content_sha256":"15bbf96f75cc62b34de6e33eb5e9c992e1a29aaeb908c71d074dccb5940ede63","schema_version":"1.0","event_id":"sha256:15bbf96f75cc62b34de6e33eb5e9c992e1a29aaeb908c71d074dccb5940ede63"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q43JDBXESTURZBQFDQ63SWWSFV/bundle.json","state_url":"https://pith.science/pith/Q43JDBXESTURZBQFDQ63SWWSFV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q43JDBXESTURZBQFDQ63SWWSFV/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":"2026-06-05T13:33:20Z","links":{"resolver":"https://pith.science/pith/Q43JDBXESTURZBQFDQ63SWWSFV","bundle":"https://pith.science/pith/Q43JDBXESTURZBQFDQ63SWWSFV/bundle.json","state":"https://pith.science/pith/Q43JDBXESTURZBQFDQ63SWWSFV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q43JDBXESTURZBQFDQ63SWWSFV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Q43JDBXESTURZBQFDQ63SWWSFV","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":"7250148ef4e4744a3521b7a086bcca83e423a45d0a00a1a60d8747a6ebf4ed00","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2018-10-31T10:24:35Z","title_canon_sha256":"63dc6028a09c241b19dee78dbbcf624a94eec36843701ff15e589484c86b9343"},"schema_version":"1.0","source":{"id":"1810.13198","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.13198","created_at":"2026-05-17T23:49:59Z"},{"alias_kind":"arxiv_version","alias_value":"1810.13198v1","created_at":"2026-05-17T23:49:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.13198","created_at":"2026-05-17T23:49:59Z"},{"alias_kind":"pith_short_12","alias_value":"Q43JDBXESTUR","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"Q43JDBXESTURZBQF","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"Q43JDBXE","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:15bbf96f75cc62b34de6e33eb5e9c992e1a29aaeb908c71d074dccb5940ede63","target":"graph","created_at":"2026-05-17T23:49:59Z","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 consider the Cauchy problem for the Volterra chain with an initial condition equal to 0 in one node and 1 in the others. It is shown that this problem admits an exact solution in terms of the Bessel functions. The Taylor series arising here are related to the exponential generating function for Catalan numbers.","authors_text":"A.B. Shabat, V.E. Adler","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2018-10-31T10:24:35Z","title":"Volterra chain and Catalan numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.13198","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:f8a5dbb369c4360d70904b305bca539aba51af8161a15e61eff7940254317b8c","target":"record","created_at":"2026-05-17T23:49:59Z","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":"7250148ef4e4744a3521b7a086bcca83e423a45d0a00a1a60d8747a6ebf4ed00","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2018-10-31T10:24:35Z","title_canon_sha256":"63dc6028a09c241b19dee78dbbcf624a94eec36843701ff15e589484c86b9343"},"schema_version":"1.0","source":{"id":"1810.13198","kind":"arxiv","version":1}},"canonical_sha256":"87369186e494e91c86051c3db95ad22d41f5e78f150fc087fed8ae123049b498","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87369186e494e91c86051c3db95ad22d41f5e78f150fc087fed8ae123049b498","first_computed_at":"2026-05-17T23:49:59.549019Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:59.549019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rOMxOMzjzw8hAXHv14LiQgvmzwQXHtgrtemERE+I3TqSMohCYs6mvKSdcnCt93baZb9LoX0MQVUZx0M4gjFTBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:59.549429Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.13198","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8a5dbb369c4360d70904b305bca539aba51af8161a15e61eff7940254317b8c","sha256:15bbf96f75cc62b34de6e33eb5e9c992e1a29aaeb908c71d074dccb5940ede63"],"state_sha256":"f6e22a21047072404fed808754ce408047b42d822150eca2118e11f59bf301a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4clgUIEz2PE41S6xNnFXY/4WZWcIJZ6VHsS8eqDGPqSFzCCCFnDfa9nEFIU1paqg7hqWrUcDbqsraRBM83/VDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T13:33:20.534082Z","bundle_sha256":"3dc245e7c5f7540dd40e510521490f23f8484937e5963208000783202c536783"}}