{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:DPQDU6YNFPUH6EV5ZWIKJFCSR6","short_pith_number":"pith:DPQDU6YN","canonical_record":{"source":{"id":"1310.2449","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-10-09T12:15:19Z","cross_cats_sorted":["cs.FL","math.CO"],"title_canon_sha256":"5fae48e1f51267166ba92833107bb897b4ed0efeb08ea2303672a20faa6ebe54","abstract_canon_sha256":"1f59d31d7f262eaa86c836b882a26964ee6b987c9b0f6a619ce629b0d89a7304"},"schema_version":"1.0"},"canonical_sha256":"1be03a7b0d2be87f12bdcd90a494528fb7418dbfe98539be5eedec56b018c6d5","source":{"kind":"arxiv","id":"1310.2449","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.2449","created_at":"2026-05-18T03:03:46Z"},{"alias_kind":"arxiv_version","alias_value":"1310.2449v2","created_at":"2026-05-18T03:03:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2449","created_at":"2026-05-18T03:03:46Z"},{"alias_kind":"pith_short_12","alias_value":"DPQDU6YNFPUH","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DPQDU6YNFPUH6EV5","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DPQDU6YN","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:DPQDU6YNFPUH6EV5ZWIKJFCSR6","target":"record","payload":{"canonical_record":{"source":{"id":"1310.2449","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-10-09T12:15:19Z","cross_cats_sorted":["cs.FL","math.CO"],"title_canon_sha256":"5fae48e1f51267166ba92833107bb897b4ed0efeb08ea2303672a20faa6ebe54","abstract_canon_sha256":"1f59d31d7f262eaa86c836b882a26964ee6b987c9b0f6a619ce629b0d89a7304"},"schema_version":"1.0"},"canonical_sha256":"1be03a7b0d2be87f12bdcd90a494528fb7418dbfe98539be5eedec56b018c6d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:46.818004Z","signature_b64":"O2z8eLMXnlqZkEHl99pRnnCDtKnoAglTF1o9lyKP4OdQe1QRQdiJ8qtMppSigcNn6ixGba4rP3MTHYlduDAZAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1be03a7b0d2be87f12bdcd90a494528fb7418dbfe98539be5eedec56b018c6d5","last_reissued_at":"2026-05-18T03:03:46.817345Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:46.817345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.2449","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:03:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4SvyCYXh2HVDu8pVytHmT2YtR91POhxoi2IPjXZ5L6JFzYr/nGXCeBsF7K9ibgVSZRKbrAZHT32IOpRKyIXGDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T20:12:37.477610Z"},"content_sha256":"02edd5882c5ac5c8f83d38a01c7bea8aec11da8e806a8ac5d0d3c3a17e801f7b","schema_version":"1.0","event_id":"sha256:02edd5882c5ac5c8f83d38a01c7bea8aec11da8e806a8ac5d0d3c3a17e801f7b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:DPQDU6YNFPUH6EV5ZWIKJFCSR6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Applications in Enumerative Combinatorics of Infinite Weighted Automata and Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL","math.CO"],"primary_cat":"cs.DM","authors_text":"Andr\\'es L. Ram\\'irez, Jos\\'e L. Ram\\'irez, Rodrigo De Castro","submitted_at":"2013-10-09T12:15:19Z","abstract_excerpt":"In this paper we studied infinite weighted automata and a general methodology to solve a wide variety of classical lattice path counting problems in an uniform way. This counting problems are related to Dyck paths, Motzkin paths and some generalizations. These methodology uses weighted automata, equations of ordinary generating functions and continued fractions. It is a variation of the one proposed by J. Rutten."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2449","kind":"arxiv","version":2},"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":"2026-05-18T03:03:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wcKIrMKQiQqp75Okh1+pb2d9afksa8hWOe1EsgW76JP2Qgd8F73rNrgJLgjggn+1/TOrd7PNNMmFUUl4Y/3iDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T20:12:37.477958Z"},"content_sha256":"4ab97af04afc9905876c8c28b6c0cfd290104a715c2392edb10c7f52b6e81e7f","schema_version":"1.0","event_id":"sha256:4ab97af04afc9905876c8c28b6c0cfd290104a715c2392edb10c7f52b6e81e7f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DPQDU6YNFPUH6EV5ZWIKJFCSR6/bundle.json","state_url":"https://pith.science/pith/DPQDU6YNFPUH6EV5ZWIKJFCSR6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DPQDU6YNFPUH6EV5ZWIKJFCSR6/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":"2026-06-03T20:12:37Z","links":{"resolver":"https://pith.science/pith/DPQDU6YNFPUH6EV5ZWIKJFCSR6","bundle":"https://pith.science/pith/DPQDU6YNFPUH6EV5ZWIKJFCSR6/bundle.json","state":"https://pith.science/pith/DPQDU6YNFPUH6EV5ZWIKJFCSR6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DPQDU6YNFPUH6EV5ZWIKJFCSR6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DPQDU6YNFPUH6EV5ZWIKJFCSR6","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":"1f59d31d7f262eaa86c836b882a26964ee6b987c9b0f6a619ce629b0d89a7304","cross_cats_sorted":["cs.FL","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-10-09T12:15:19Z","title_canon_sha256":"5fae48e1f51267166ba92833107bb897b4ed0efeb08ea2303672a20faa6ebe54"},"schema_version":"1.0","source":{"id":"1310.2449","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.2449","created_at":"2026-05-18T03:03:46Z"},{"alias_kind":"arxiv_version","alias_value":"1310.2449v2","created_at":"2026-05-18T03:03:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2449","created_at":"2026-05-18T03:03:46Z"},{"alias_kind":"pith_short_12","alias_value":"DPQDU6YNFPUH","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DPQDU6YNFPUH6EV5","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DPQDU6YN","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:4ab97af04afc9905876c8c28b6c0cfd290104a715c2392edb10c7f52b6e81e7f","target":"graph","created_at":"2026-05-18T03:03:46Z","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":"In this paper we studied infinite weighted automata and a general methodology to solve a wide variety of classical lattice path counting problems in an uniform way. This counting problems are related to Dyck paths, Motzkin paths and some generalizations. These methodology uses weighted automata, equations of ordinary generating functions and continued fractions. It is a variation of the one proposed by J. Rutten.","authors_text":"Andr\\'es L. Ram\\'irez, Jos\\'e L. Ram\\'irez, Rodrigo De Castro","cross_cats":["cs.FL","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-10-09T12:15:19Z","title":"Applications in Enumerative Combinatorics of Infinite Weighted Automata and Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2449","kind":"arxiv","version":2},"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":"sha256:02edd5882c5ac5c8f83d38a01c7bea8aec11da8e806a8ac5d0d3c3a17e801f7b","target":"record","created_at":"2026-05-18T03:03:46Z","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":"1f59d31d7f262eaa86c836b882a26964ee6b987c9b0f6a619ce629b0d89a7304","cross_cats_sorted":["cs.FL","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-10-09T12:15:19Z","title_canon_sha256":"5fae48e1f51267166ba92833107bb897b4ed0efeb08ea2303672a20faa6ebe54"},"schema_version":"1.0","source":{"id":"1310.2449","kind":"arxiv","version":2}},"canonical_sha256":"1be03a7b0d2be87f12bdcd90a494528fb7418dbfe98539be5eedec56b018c6d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1be03a7b0d2be87f12bdcd90a494528fb7418dbfe98539be5eedec56b018c6d5","first_computed_at":"2026-05-18T03:03:46.817345Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:46.817345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O2z8eLMXnlqZkEHl99pRnnCDtKnoAglTF1o9lyKP4OdQe1QRQdiJ8qtMppSigcNn6ixGba4rP3MTHYlduDAZAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:46.818004Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.2449","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02edd5882c5ac5c8f83d38a01c7bea8aec11da8e806a8ac5d0d3c3a17e801f7b","sha256:4ab97af04afc9905876c8c28b6c0cfd290104a715c2392edb10c7f52b6e81e7f"],"state_sha256":"d18c308d1da37892e7cbe34a4873b733d9e523060a172b76fe451d4e3806b5be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lb13wvSau1xuWAS4DR/zmT1Jrv1/Lx/F0+sOnyilz6ueYLmoA+peR4BNnFKZyelTrv21XO9fVjur5aWyDPwNBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T20:12:37.479957Z","bundle_sha256":"76784817e13e9ddb5648c59042cd2466822970bb8e14d39e6a162880d17dd55f"}}