{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:XAMIBF56Y6WRRQRICVIFDNUBEJ","short_pith_number":"pith:XAMIBF56","canonical_record":{"source":{"id":"1105.0957","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-04T21:57:10Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"5e2863e0e47de9d1dda17580e1f52621c92db62cc498c7f81081c50f040c703a","abstract_canon_sha256":"70e8596bdd126b8bed504efe2d656837aff735d6cae2f03e9361ef9226071d86"},"schema_version":"1.0"},"canonical_sha256":"b8188097bec7ad18c228155051b6812248ef424963d2f9116a2224cd8ab5b158","source":{"kind":"arxiv","id":"1105.0957","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.0957","created_at":"2026-05-18T04:22:49Z"},{"alias_kind":"arxiv_version","alias_value":"1105.0957v1","created_at":"2026-05-18T04:22:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.0957","created_at":"2026-05-18T04:22:49Z"},{"alias_kind":"pith_short_12","alias_value":"XAMIBF56Y6WR","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XAMIBF56Y6WRRQRI","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XAMIBF56","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:XAMIBF56Y6WRRQRICVIFDNUBEJ","target":"record","payload":{"canonical_record":{"source":{"id":"1105.0957","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-04T21:57:10Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"5e2863e0e47de9d1dda17580e1f52621c92db62cc498c7f81081c50f040c703a","abstract_canon_sha256":"70e8596bdd126b8bed504efe2d656837aff735d6cae2f03e9361ef9226071d86"},"schema_version":"1.0"},"canonical_sha256":"b8188097bec7ad18c228155051b6812248ef424963d2f9116a2224cd8ab5b158","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:49.591771Z","signature_b64":"z8TN+6HqlhsqNx+phXL2SxwrSzmq34Ljw1UcJqpYW1McaTWjv2xQfYyCkbnYNmNfF7Ohux+NxwMwtkZ5Jxc+DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8188097bec7ad18c228155051b6812248ef424963d2f9116a2224cd8ab5b158","last_reissued_at":"2026-05-18T04:22:49.591051Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:49.591051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.0957","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":"2026-05-18T04:22:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ig97tU8DQwBz9Qf1/Z9dVgvC5ZbCWhub7/0FykhaI8LGMXTW0mMDV8s9pJ3jHU+Mdljd3eJpGAq8+ntNlOgCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:39:51.922974Z"},"content_sha256":"aa3106a92d7ccdd4007341b7fcdf4990c6f72ab29cc80bd94fab5ceb09b1819e","schema_version":"1.0","event_id":"sha256:aa3106a92d7ccdd4007341b7fcdf4990c6f72ab29cc80bd94fab5ceb09b1819e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:XAMIBF56Y6WRRQRICVIFDNUBEJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximate closed-form formulas for the zeros of the Bessel Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Marisol L. Calderon, Rafael G. Campos","submitted_at":"2011-05-04T21:57:10Z","abstract_excerpt":"We find approximate expressions x(k,n) and y(k,n) for the real and imaginary parts of the kth zero z_k=x_k+i y_k of the Bessel polynomial y_n(x). To obtain these closed-form formulas we use the fact that the points of well-defined curves in the complex plane are limit points of the zeros of the normalized Bessel polynomials. Thus, these zeros are first computed numerically through an implementation of the electrostatic interpretation formulas and then, a fit to the real and imaginary parts as functions of k and n is obtained. It is shown that the resulting complex number x(k,n)+i y(k,n) is O(1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0957","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":"2026-05-18T04:22:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TBUsQSwqJ4A66zdey3/8GAIjhoZ8aq7dQ1MLbtfgFb/5RfphfJzGJC75DDLmr/uwMn8AzeRwoas+ghp6k1c7Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:39:51.923698Z"},"content_sha256":"32e70a9e627908da6a66fedc84edd390c4e947b0d1005bfadf5fe4c09bb8a8c8","schema_version":"1.0","event_id":"sha256:32e70a9e627908da6a66fedc84edd390c4e947b0d1005bfadf5fe4c09bb8a8c8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XAMIBF56Y6WRRQRICVIFDNUBEJ/bundle.json","state_url":"https://pith.science/pith/XAMIBF56Y6WRRQRICVIFDNUBEJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XAMIBF56Y6WRRQRICVIFDNUBEJ/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":"2026-06-11T22:39:51Z","links":{"resolver":"https://pith.science/pith/XAMIBF56Y6WRRQRICVIFDNUBEJ","bundle":"https://pith.science/pith/XAMIBF56Y6WRRQRICVIFDNUBEJ/bundle.json","state":"https://pith.science/pith/XAMIBF56Y6WRRQRICVIFDNUBEJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XAMIBF56Y6WRRQRICVIFDNUBEJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XAMIBF56Y6WRRQRICVIFDNUBEJ","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":"70e8596bdd126b8bed504efe2d656837aff735d6cae2f03e9361ef9226071d86","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-04T21:57:10Z","title_canon_sha256":"5e2863e0e47de9d1dda17580e1f52621c92db62cc498c7f81081c50f040c703a"},"schema_version":"1.0","source":{"id":"1105.0957","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.0957","created_at":"2026-05-18T04:22:49Z"},{"alias_kind":"arxiv_version","alias_value":"1105.0957v1","created_at":"2026-05-18T04:22:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.0957","created_at":"2026-05-18T04:22:49Z"},{"alias_kind":"pith_short_12","alias_value":"XAMIBF56Y6WR","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XAMIBF56Y6WRRQRI","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XAMIBF56","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:32e70a9e627908da6a66fedc84edd390c4e947b0d1005bfadf5fe4c09bb8a8c8","target":"graph","created_at":"2026-05-18T04:22:49Z","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 find approximate expressions x(k,n) and y(k,n) for the real and imaginary parts of the kth zero z_k=x_k+i y_k of the Bessel polynomial y_n(x). To obtain these closed-form formulas we use the fact that the points of well-defined curves in the complex plane are limit points of the zeros of the normalized Bessel polynomials. Thus, these zeros are first computed numerically through an implementation of the electrostatic interpretation formulas and then, a fit to the real and imaginary parts as functions of k and n is obtained. It is shown that the resulting complex number x(k,n)+i y(k,n) is O(1","authors_text":"Marisol L. Calderon, Rafael G. Campos","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-04T21:57:10Z","title":"Approximate closed-form formulas for the zeros of the Bessel Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0957","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:aa3106a92d7ccdd4007341b7fcdf4990c6f72ab29cc80bd94fab5ceb09b1819e","target":"record","created_at":"2026-05-18T04:22:49Z","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":"70e8596bdd126b8bed504efe2d656837aff735d6cae2f03e9361ef9226071d86","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-04T21:57:10Z","title_canon_sha256":"5e2863e0e47de9d1dda17580e1f52621c92db62cc498c7f81081c50f040c703a"},"schema_version":"1.0","source":{"id":"1105.0957","kind":"arxiv","version":1}},"canonical_sha256":"b8188097bec7ad18c228155051b6812248ef424963d2f9116a2224cd8ab5b158","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8188097bec7ad18c228155051b6812248ef424963d2f9116a2224cd8ab5b158","first_computed_at":"2026-05-18T04:22:49.591051Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:49.591051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z8TN+6HqlhsqNx+phXL2SxwrSzmq34Ljw1UcJqpYW1McaTWjv2xQfYyCkbnYNmNfF7Ohux+NxwMwtkZ5Jxc+DA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:49.591771Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.0957","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa3106a92d7ccdd4007341b7fcdf4990c6f72ab29cc80bd94fab5ceb09b1819e","sha256:32e70a9e627908da6a66fedc84edd390c4e947b0d1005bfadf5fe4c09bb8a8c8"],"state_sha256":"e30de3f5a5a05d5197fb5659f6c99088e1cef141a65ede7107949c8055493b7d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0pIw8RSCzfsKrm8fQ/oZIZWJcaETmQqqmpm8yIwEgmmyXw8IfPOs4fh++qv61Ra+lA/aGKkGJy7uSp1LSuGeCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T22:39:51.927493Z","bundle_sha256":"0c14ddf1f4db730dff1c159a000a7523efc6bd5502205230ef7bed9472afab8f"}}