{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:7IUXYVZ6GW5JCSQ22DF7P3SKMK","short_pith_number":"pith:7IUXYVZ6","canonical_record":{"source":{"id":"1506.05734","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-18T16:07:15Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"fbdb98abcbaf1b191c7d820e83acb001f879fd6d2767285962df73f77e5f1d3a","abstract_canon_sha256":"0693c6d66f5b14bdff160adb3e821607fc8c1fdf64b25bf23b2ee02c396d411d"},"schema_version":"1.0"},"canonical_sha256":"fa297c573e35ba914a1ad0cbf7ee4a62a1266e43689c371e9930c4383da5266b","source":{"kind":"arxiv","id":"1506.05734","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.05734","created_at":"2026-05-18T01:11:27Z"},{"alias_kind":"arxiv_version","alias_value":"1506.05734v1","created_at":"2026-05-18T01:11:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.05734","created_at":"2026-05-18T01:11:27Z"},{"alias_kind":"pith_short_12","alias_value":"7IUXYVZ6GW5J","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7IUXYVZ6GW5JCSQ2","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7IUXYVZ6","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:7IUXYVZ6GW5JCSQ22DF7P3SKMK","target":"record","payload":{"canonical_record":{"source":{"id":"1506.05734","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-18T16:07:15Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"fbdb98abcbaf1b191c7d820e83acb001f879fd6d2767285962df73f77e5f1d3a","abstract_canon_sha256":"0693c6d66f5b14bdff160adb3e821607fc8c1fdf64b25bf23b2ee02c396d411d"},"schema_version":"1.0"},"canonical_sha256":"fa297c573e35ba914a1ad0cbf7ee4a62a1266e43689c371e9930c4383da5266b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:27.361633Z","signature_b64":"UXmin0d8KnbiOWdfZSd3b0R14+JhLHXmKBEQOxlmBe6A69SPK97v81wR9rHrCXQVa/fLcjUtzvh3naaBhs3SDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa297c573e35ba914a1ad0cbf7ee4a62a1266e43689c371e9930c4383da5266b","last_reissued_at":"2026-05-18T01:11:27.360913Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:27.360913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.05734","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":"2026-05-18T01:11:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ok/st24l4Woapj0HnWdG1/L3NNdMniq5ddQDGJblAq4JWZogeUuVn3meWCNAfeyjP/jsz2m3OvGTlfmYWtuBCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T01:13:33.703627Z"},"content_sha256":"c2f11da0967d31c59445e046ef721a8c1cc42d4de0cf101296e155405d398d59","schema_version":"1.0","event_id":"sha256:c2f11da0967d31c59445e046ef721a8c1cc42d4de0cf101296e155405d398d59"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:7IUXYVZ6GW5JCSQ22DF7P3SKMK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Orthogonal polynomials for the weakly equilibrium Cantor sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Alexander Goncharov, Gokalp Alpan","submitted_at":"2015-06-18T16:07:15Z","abstract_excerpt":"Let $K(\\gamma)$ be the weakly equilibrium Cantor type set introduced in [10]. It is proven that the monic orthogonal polynomials $Q_{2^s}$ with respect to the equilibrium measure of $K(\\gamma)$ coincide with the Chebyshev polynomials of the set. Procedures are suggested to find $Q_{n}$ of all degrees and the corresponding Jacobi parameters. It is shown that the sequence of the Widom factors is bounded below."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05734","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":"2026-05-18T01:11:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Av7ueNHN2PdHXZaKD7I0HnWM1FXJtgXGHZNMZo2lOjwCmXX7yPrkdp9SuqcDeJvvrh3lF+w1b/aByXwDOJobBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T01:13:33.704348Z"},"content_sha256":"fa6606be2c3074a46e31a6ba8ddfb6b12178edf1ea7babb42e8e9b0746890d9b","schema_version":"1.0","event_id":"sha256:fa6606be2c3074a46e31a6ba8ddfb6b12178edf1ea7babb42e8e9b0746890d9b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7IUXYVZ6GW5JCSQ22DF7P3SKMK/bundle.json","state_url":"https://pith.science/pith/7IUXYVZ6GW5JCSQ22DF7P3SKMK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7IUXYVZ6GW5JCSQ22DF7P3SKMK/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":"2026-05-30T01:13:33Z","links":{"resolver":"https://pith.science/pith/7IUXYVZ6GW5JCSQ22DF7P3SKMK","bundle":"https://pith.science/pith/7IUXYVZ6GW5JCSQ22DF7P3SKMK/bundle.json","state":"https://pith.science/pith/7IUXYVZ6GW5JCSQ22DF7P3SKMK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7IUXYVZ6GW5JCSQ22DF7P3SKMK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7IUXYVZ6GW5JCSQ22DF7P3SKMK","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":"0693c6d66f5b14bdff160adb3e821607fc8c1fdf64b25bf23b2ee02c396d411d","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-18T16:07:15Z","title_canon_sha256":"fbdb98abcbaf1b191c7d820e83acb001f879fd6d2767285962df73f77e5f1d3a"},"schema_version":"1.0","source":{"id":"1506.05734","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.05734","created_at":"2026-05-18T01:11:27Z"},{"alias_kind":"arxiv_version","alias_value":"1506.05734v1","created_at":"2026-05-18T01:11:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.05734","created_at":"2026-05-18T01:11:27Z"},{"alias_kind":"pith_short_12","alias_value":"7IUXYVZ6GW5J","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7IUXYVZ6GW5JCSQ2","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7IUXYVZ6","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:fa6606be2c3074a46e31a6ba8ddfb6b12178edf1ea7babb42e8e9b0746890d9b","target":"graph","created_at":"2026-05-18T01:11:27Z","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":"Let $K(\\gamma)$ be the weakly equilibrium Cantor type set introduced in [10]. It is proven that the monic orthogonal polynomials $Q_{2^s}$ with respect to the equilibrium measure of $K(\\gamma)$ coincide with the Chebyshev polynomials of the set. Procedures are suggested to find $Q_{n}$ of all degrees and the corresponding Jacobi parameters. It is shown that the sequence of the Widom factors is bounded below.","authors_text":"Alexander Goncharov, Gokalp Alpan","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-18T16:07:15Z","title":"Orthogonal polynomials for the weakly equilibrium Cantor sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05734","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:c2f11da0967d31c59445e046ef721a8c1cc42d4de0cf101296e155405d398d59","target":"record","created_at":"2026-05-18T01:11:27Z","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":"0693c6d66f5b14bdff160adb3e821607fc8c1fdf64b25bf23b2ee02c396d411d","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-18T16:07:15Z","title_canon_sha256":"fbdb98abcbaf1b191c7d820e83acb001f879fd6d2767285962df73f77e5f1d3a"},"schema_version":"1.0","source":{"id":"1506.05734","kind":"arxiv","version":1}},"canonical_sha256":"fa297c573e35ba914a1ad0cbf7ee4a62a1266e43689c371e9930c4383da5266b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa297c573e35ba914a1ad0cbf7ee4a62a1266e43689c371e9930c4383da5266b","first_computed_at":"2026-05-18T01:11:27.360913Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:27.360913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UXmin0d8KnbiOWdfZSd3b0R14+JhLHXmKBEQOxlmBe6A69SPK97v81wR9rHrCXQVa/fLcjUtzvh3naaBhs3SDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:27.361633Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.05734","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2f11da0967d31c59445e046ef721a8c1cc42d4de0cf101296e155405d398d59","sha256:fa6606be2c3074a46e31a6ba8ddfb6b12178edf1ea7babb42e8e9b0746890d9b"],"state_sha256":"69c68a7730285b163e99ce571d4acce184593d55c382f356d10ad149c68b64ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4jaIgilshwctqm48dht9MbQ0ruQBR/XltXBtadJsOwE8EPHgJEyYUI7xcRBNmQEtkHGSyb2ao3Y6XRLlXsy0AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T01:13:33.709209Z","bundle_sha256":"c20f8df8ace3678e2dfc8a445ecdf822e8a389c62596355be32e3d866cae06c2"}}