{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1994:J7L5DBB7W5RNLIOQZJRR7O4RR6","short_pith_number":"pith:J7L5DBB7","canonical_record":{"source":{"id":"math/9406224","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"1994-06-07T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"4d230e8b74e9b25d6361ec951f89b9348aaedbba00c2bdf11d6fd0e3d98ef139","abstract_canon_sha256":"490723bc7b5cc75d351481ecbf7213b8c131e48a69ab481dd07a4683a7061539"},"schema_version":"1.0"},"canonical_sha256":"4fd7d1843fb762d5a1d0ca631fbb918f89f9759339a7840320e7f91182deb38b","source":{"kind":"arxiv","id":"math/9406224","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9406224","created_at":"2026-05-18T01:05:51Z"},{"alias_kind":"arxiv_version","alias_value":"math/9406224v1","created_at":"2026-05-18T01:05:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9406224","created_at":"2026-05-18T01:05:51Z"},{"alias_kind":"pith_short_12","alias_value":"J7L5DBB7W5RN","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"J7L5DBB7W5RNLIOQ","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"J7L5DBB7","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1994:J7L5DBB7W5RNLIOQZJRR7O4RR6","target":"record","payload":{"canonical_record":{"source":{"id":"math/9406224","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"1994-06-07T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"4d230e8b74e9b25d6361ec951f89b9348aaedbba00c2bdf11d6fd0e3d98ef139","abstract_canon_sha256":"490723bc7b5cc75d351481ecbf7213b8c131e48a69ab481dd07a4683a7061539"},"schema_version":"1.0"},"canonical_sha256":"4fd7d1843fb762d5a1d0ca631fbb918f89f9759339a7840320e7f91182deb38b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:51.318993Z","signature_b64":"gaTlSKudklwQLcTtKEhg4f8TnRcnNqb7RDWwFzOTyakAnfNM4mXmzl22J24hnHMF5GeVjAr+GVzmddz1og4PAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fd7d1843fb762d5a1d0ca631fbb918f89f9759339a7840320e7f91182deb38b","last_reissued_at":"2026-05-18T01:05:51.318426Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:51.318426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9406224","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":"2026-05-18T01:05:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rPrFMnNxFmKAP41TMLglXARCHKwMLJIhbgp1EXhymWl+X01kS3G4IKSAJkZVi04NTMYn6FnW4oDNU+SDlMw2AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:58:58.100681Z"},"content_sha256":"81b4db733ae1dd40bf1a6911e61f6ceddeb29725b6dfbbc9d34eca9d80d05b82","schema_version":"1.0","event_id":"sha256:81b4db733ae1dd40bf1a6911e61f6ceddeb29725b6dfbbc9d34eca9d80d05b82"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1994:J7L5DBB7W5RNLIOQZJRR7O4RR6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some new asymptotic properties for the zeros of Jacobi, Laguerre and Hermite polynomials","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Holger Dette, William J. Studden","submitted_at":"1994-06-07T00:00:00Z","abstract_excerpt":"For the generalized Jacobi, Laguerre and Hermite polynomials $P_n^{(\\alpha_n, \\beta_n)} (x), L_n^{(\\alpha_n)} (x),$\\break $H_n^{(\\gamma_n)} (x)$ the limit distributions of the zeros are found, when the sequences $\\alpha_n$ or $\\beta_n$ tend to infinity with a larger order than $n$. The derivation uses special properties of the sequences in the corresponding recurrence formulae. The results are used to give second order approximations for the largest and smallest zero which improve (and generalize) the limit statements in a paper of Moak, Saff and Varga [11]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9406224","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":"2026-05-18T01:05:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IWgKh37vCgWixAQL7Dl//9SH23fvMJfqNjKHlnTEmckq0o8H/IiNasshA88TY4b2FXId5qsfNkmgSsnx/ljmBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:58:58.101028Z"},"content_sha256":"71b4af4523ff2d5519da0bfeaf83ee647c28c395571d4997759d4f7da8bbb8bf","schema_version":"1.0","event_id":"sha256:71b4af4523ff2d5519da0bfeaf83ee647c28c395571d4997759d4f7da8bbb8bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J7L5DBB7W5RNLIOQZJRR7O4RR6/bundle.json","state_url":"https://pith.science/pith/J7L5DBB7W5RNLIOQZJRR7O4RR6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J7L5DBB7W5RNLIOQZJRR7O4RR6/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":"2026-06-02T22:58:58Z","links":{"resolver":"https://pith.science/pith/J7L5DBB7W5RNLIOQZJRR7O4RR6","bundle":"https://pith.science/pith/J7L5DBB7W5RNLIOQZJRR7O4RR6/bundle.json","state":"https://pith.science/pith/J7L5DBB7W5RNLIOQZJRR7O4RR6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J7L5DBB7W5RNLIOQZJRR7O4RR6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1994:J7L5DBB7W5RNLIOQZJRR7O4RR6","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":"490723bc7b5cc75d351481ecbf7213b8c131e48a69ab481dd07a4683a7061539","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"1994-06-07T00:00:00Z","title_canon_sha256":"4d230e8b74e9b25d6361ec951f89b9348aaedbba00c2bdf11d6fd0e3d98ef139"},"schema_version":"1.0","source":{"id":"math/9406224","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9406224","created_at":"2026-05-18T01:05:51Z"},{"alias_kind":"arxiv_version","alias_value":"math/9406224v1","created_at":"2026-05-18T01:05:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9406224","created_at":"2026-05-18T01:05:51Z"},{"alias_kind":"pith_short_12","alias_value":"J7L5DBB7W5RN","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"J7L5DBB7W5RNLIOQ","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"J7L5DBB7","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:71b4af4523ff2d5519da0bfeaf83ee647c28c395571d4997759d4f7da8bbb8bf","target":"graph","created_at":"2026-05-18T01:05:51Z","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":"For the generalized Jacobi, Laguerre and Hermite polynomials $P_n^{(\\alpha_n, \\beta_n)} (x), L_n^{(\\alpha_n)} (x),$\\break $H_n^{(\\gamma_n)} (x)$ the limit distributions of the zeros are found, when the sequences $\\alpha_n$ or $\\beta_n$ tend to infinity with a larger order than $n$. The derivation uses special properties of the sequences in the corresponding recurrence formulae. The results are used to give second order approximations for the largest and smallest zero which improve (and generalize) the limit statements in a paper of Moak, Saff and Varga [11].","authors_text":"Holger Dette, William J. Studden","cross_cats":[],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"1994-06-07T00:00:00Z","title":"Some new asymptotic properties for the zeros of Jacobi, Laguerre and Hermite polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9406224","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":"sha256:81b4db733ae1dd40bf1a6911e61f6ceddeb29725b6dfbbc9d34eca9d80d05b82","target":"record","created_at":"2026-05-18T01:05:51Z","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":"490723bc7b5cc75d351481ecbf7213b8c131e48a69ab481dd07a4683a7061539","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"1994-06-07T00:00:00Z","title_canon_sha256":"4d230e8b74e9b25d6361ec951f89b9348aaedbba00c2bdf11d6fd0e3d98ef139"},"schema_version":"1.0","source":{"id":"math/9406224","kind":"arxiv","version":1}},"canonical_sha256":"4fd7d1843fb762d5a1d0ca631fbb918f89f9759339a7840320e7f91182deb38b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4fd7d1843fb762d5a1d0ca631fbb918f89f9759339a7840320e7f91182deb38b","first_computed_at":"2026-05-18T01:05:51.318426Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:51.318426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gaTlSKudklwQLcTtKEhg4f8TnRcnNqb7RDWwFzOTyakAnfNM4mXmzl22J24hnHMF5GeVjAr+GVzmddz1og4PAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:51.318993Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9406224","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81b4db733ae1dd40bf1a6911e61f6ceddeb29725b6dfbbc9d34eca9d80d05b82","sha256:71b4af4523ff2d5519da0bfeaf83ee647c28c395571d4997759d4f7da8bbb8bf"],"state_sha256":"7c46e3903212c40361476af0da5b775d87e0b363ce8183007c0d0382bf62e64e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UIvYTQD9KajsMj0vh1VJj0LXUTz7buJRnF6CcTfQi0gpJoacs9bSoZMqT2vFf999YZ8zMZ6MQ3THMbPvg6CcAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T22:58:58.103022Z","bundle_sha256":"0c112360fa3a163b787cd26d112920c7b4a452bc473c798df475cdc6dd97a42f"}}