{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CCIIUT6ZI4DZJ44N6A2QFHIK5T","short_pith_number":"pith:CCIIUT6Z","canonical_record":{"source":{"id":"1707.04654","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2017-07-14T22:12:18Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"ab628d0ef0fe02b001defa4cceba273a0ccc6ede012fa0c22f4ee1bcc97a44d9","abstract_canon_sha256":"4deadce28c53a39c2bbea4b5b5177c39ad7ce3f6cc991c2e092ca0005e0118a3"},"schema_version":"1.0"},"canonical_sha256":"10908a4fd9470794f38df035029d0aeceab700008b7a14a21d84f58258187ab9","source":{"kind":"arxiv","id":"1707.04654","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.04654","created_at":"2026-05-18T00:32:20Z"},{"alias_kind":"arxiv_version","alias_value":"1707.04654v2","created_at":"2026-05-18T00:32:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.04654","created_at":"2026-05-18T00:32:20Z"},{"alias_kind":"pith_short_12","alias_value":"CCIIUT6ZI4DZ","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CCIIUT6ZI4DZJ44N","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CCIIUT6Z","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CCIIUT6ZI4DZJ44N6A2QFHIK5T","target":"record","payload":{"canonical_record":{"source":{"id":"1707.04654","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2017-07-14T22:12:18Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"ab628d0ef0fe02b001defa4cceba273a0ccc6ede012fa0c22f4ee1bcc97a44d9","abstract_canon_sha256":"4deadce28c53a39c2bbea4b5b5177c39ad7ce3f6cc991c2e092ca0005e0118a3"},"schema_version":"1.0"},"canonical_sha256":"10908a4fd9470794f38df035029d0aeceab700008b7a14a21d84f58258187ab9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:20.317591Z","signature_b64":"Yq3YEMhVQyUThWxIqjePDIdo3bQItGR0nSL4jJP2Zq7/fOBaJNLgdlrWBrWPqbv/sqhp6OpHYMGyLnvT+o7oDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10908a4fd9470794f38df035029d0aeceab700008b7a14a21d84f58258187ab9","last_reissued_at":"2026-05-18T00:32:20.316845Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:20.316845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.04654","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":"2026-05-18T00:32:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7sbfmmbct1D3kG17+pTZfEBB26/WxxU+ut5S1FadldWAJYtZJQwqRdatw53DKb08AqZumZyLz1afXFmiUhwdDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:30:20.500951Z"},"content_sha256":"7dfb678ae01a28cae9af9a78dc75680829376f7a6ad7c807b3296dd29e6162ea","schema_version":"1.0","event_id":"sha256:7dfb678ae01a28cae9af9a78dc75680829376f7a6ad7c807b3296dd29e6162ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CCIIUT6ZI4DZJ44N6A2QFHIK5T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Automated Proofs of Many Conjectured Recurrences in the OEIS made by R.J. Mathar","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.HO","authors_text":"Doron Zeilberger, Mingjia Yang, Shalosh B. Ekhad","submitted_at":"2017-07-14T22:12:18Z","abstract_excerpt":"The On-Line Encyclopedia Of Integer Sequences , that wonderful resource that most combinatorialists, and many other mathematicians and scientists, use at least once a day, is a treasure trove of mathematical information, and, one of its charms is that it contains many intriguing conjectures. But one should be on one's guard, because some of the conjectures are either already theorems, or can be routinely proved. In this case study we demonstrate, and actually fully implement (in an accompanying Maple package), how to turn many conjectures made in the OEIS by R.J. Mathar, regarding linear recur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04654","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":"2026-05-18T00:32:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6gMy5W1EJ63NVLQ7JDt9JKpcqoYs30u2PQubeX3NpVt7fy0plhbPIhvNDk72KdoWT2/dORj4r3Ehpb0TBo2+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:30:20.501668Z"},"content_sha256":"693478182a65070be511c0365ce43acc5bbf7571d02dddd308fd77ea78751d58","schema_version":"1.0","event_id":"sha256:693478182a65070be511c0365ce43acc5bbf7571d02dddd308fd77ea78751d58"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CCIIUT6ZI4DZJ44N6A2QFHIK5T/bundle.json","state_url":"https://pith.science/pith/CCIIUT6ZI4DZJ44N6A2QFHIK5T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CCIIUT6ZI4DZJ44N6A2QFHIK5T/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":"2026-05-30T05:30:20Z","links":{"resolver":"https://pith.science/pith/CCIIUT6ZI4DZJ44N6A2QFHIK5T","bundle":"https://pith.science/pith/CCIIUT6ZI4DZJ44N6A2QFHIK5T/bundle.json","state":"https://pith.science/pith/CCIIUT6ZI4DZJ44N6A2QFHIK5T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CCIIUT6ZI4DZJ44N6A2QFHIK5T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CCIIUT6ZI4DZJ44N6A2QFHIK5T","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":"4deadce28c53a39c2bbea4b5b5177c39ad7ce3f6cc991c2e092ca0005e0118a3","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2017-07-14T22:12:18Z","title_canon_sha256":"ab628d0ef0fe02b001defa4cceba273a0ccc6ede012fa0c22f4ee1bcc97a44d9"},"schema_version":"1.0","source":{"id":"1707.04654","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.04654","created_at":"2026-05-18T00:32:20Z"},{"alias_kind":"arxiv_version","alias_value":"1707.04654v2","created_at":"2026-05-18T00:32:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.04654","created_at":"2026-05-18T00:32:20Z"},{"alias_kind":"pith_short_12","alias_value":"CCIIUT6ZI4DZ","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CCIIUT6ZI4DZJ44N","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CCIIUT6Z","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:693478182a65070be511c0365ce43acc5bbf7571d02dddd308fd77ea78751d58","target":"graph","created_at":"2026-05-18T00:32:20Z","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":"The On-Line Encyclopedia Of Integer Sequences , that wonderful resource that most combinatorialists, and many other mathematicians and scientists, use at least once a day, is a treasure trove of mathematical information, and, one of its charms is that it contains many intriguing conjectures. But one should be on one's guard, because some of the conjectures are either already theorems, or can be routinely proved. In this case study we demonstrate, and actually fully implement (in an accompanying Maple package), how to turn many conjectures made in the OEIS by R.J. Mathar, regarding linear recur","authors_text":"Doron Zeilberger, Mingjia Yang, Shalosh B. Ekhad","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2017-07-14T22:12:18Z","title":"Automated Proofs of Many Conjectured Recurrences in the OEIS made by R.J. Mathar"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04654","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":"sha256:7dfb678ae01a28cae9af9a78dc75680829376f7a6ad7c807b3296dd29e6162ea","target":"record","created_at":"2026-05-18T00:32:20Z","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":"4deadce28c53a39c2bbea4b5b5177c39ad7ce3f6cc991c2e092ca0005e0118a3","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2017-07-14T22:12:18Z","title_canon_sha256":"ab628d0ef0fe02b001defa4cceba273a0ccc6ede012fa0c22f4ee1bcc97a44d9"},"schema_version":"1.0","source":{"id":"1707.04654","kind":"arxiv","version":2}},"canonical_sha256":"10908a4fd9470794f38df035029d0aeceab700008b7a14a21d84f58258187ab9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10908a4fd9470794f38df035029d0aeceab700008b7a14a21d84f58258187ab9","first_computed_at":"2026-05-18T00:32:20.316845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:20.316845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yq3YEMhVQyUThWxIqjePDIdo3bQItGR0nSL4jJP2Zq7/fOBaJNLgdlrWBrWPqbv/sqhp6OpHYMGyLnvT+o7oDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:20.317591Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.04654","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7dfb678ae01a28cae9af9a78dc75680829376f7a6ad7c807b3296dd29e6162ea","sha256:693478182a65070be511c0365ce43acc5bbf7571d02dddd308fd77ea78751d58"],"state_sha256":"e6b4e18d951b4f0053aaa79556ab8bae74afe797d26be17390f0e8d6085ee0fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kLlqjUvJxKzp8OSdR+QsAb0vMyBxWq9ToJNGTXDlvZh2JHJWGRd2IQYxcAwjK0rWv/acU86+VsaReMeEyhbKBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T05:30:20.508204Z","bundle_sha256":"aabf3e8d57bb3d345fa51f1ffb8617125fc39b54459f579cb9fc3c6b7e2eebd6"}}