{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:TB34NZSDKIQDKI5EA2XLZZYVAI","short_pith_number":"pith:TB34NZSD","canonical_record":{"source":{"id":"1305.3071","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-14T09:08:32Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"51d1c6d2dc2fbc0ab4881778a73356b7b185b6f501e0f299d0e180b6f51fb21d","abstract_canon_sha256":"71331e0b1a80d58f438ce492ad0d6985759eaf5539de1ff05393ed6b0949b2bf"},"schema_version":"1.0"},"canonical_sha256":"9877c6e64352203523a406aebce715020d5b07ab8f69bce6e627ae21601edad6","source":{"kind":"arxiv","id":"1305.3071","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.3071","created_at":"2026-05-18T03:25:44Z"},{"alias_kind":"arxiv_version","alias_value":"1305.3071v1","created_at":"2026-05-18T03:25:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3071","created_at":"2026-05-18T03:25:44Z"},{"alias_kind":"pith_short_12","alias_value":"TB34NZSDKIQD","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"TB34NZSDKIQDKI5E","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"TB34NZSD","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:TB34NZSDKIQDKI5EA2XLZZYVAI","target":"record","payload":{"canonical_record":{"source":{"id":"1305.3071","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-14T09:08:32Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"51d1c6d2dc2fbc0ab4881778a73356b7b185b6f501e0f299d0e180b6f51fb21d","abstract_canon_sha256":"71331e0b1a80d58f438ce492ad0d6985759eaf5539de1ff05393ed6b0949b2bf"},"schema_version":"1.0"},"canonical_sha256":"9877c6e64352203523a406aebce715020d5b07ab8f69bce6e627ae21601edad6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:44.935220Z","signature_b64":"06bcFcMHns0MK5pUXAkcopcH+xX2efP4iSVlkSAEyzTuwxVR2m1RfTH3JtEmtrBdCLfyhmDf3087cZDsgym4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9877c6e64352203523a406aebce715020d5b07ab8f69bce6e627ae21601edad6","last_reissued_at":"2026-05-18T03:25:44.934380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:44.934380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.3071","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":"2026-05-18T03:25:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ytXBBeVLuw31Tv6iHDQzD/6/tNG1mvHsbYK+1BaR6Yy/cA45cuJxgW7nTWglgMO9Mj5zeEmaGzSlXhnKEUbzBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T21:35:35.649522Z"},"content_sha256":"ba5f1ffee08d9503ad2593401b2ee50a3064f0b0ab2e1a9321f04837a728f363","schema_version":"1.0","event_id":"sha256:ba5f1ffee08d9503ad2593401b2ee50a3064f0b0ab2e1a9321f04837a728f363"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:TB34NZSDKIQDKI5EA2XLZZYVAI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotics of $L_p$-norms of Hermite polynomials and R\\'enyi entropy of Rydberg oscillator states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alexander I. Aptekarev, Dmitrii N. Tulyakov, Jes\\'us S. Dehesa, Pablo S\\'anchez-Moreno","submitted_at":"2013-05-14T09:08:32Z","abstract_excerpt":"The asymptotics of the weighted $L_{p}$-norms of Hermite polynomials, which describes the R\\'enyi entropy of order $p$ of the associated quantum oscillator probability density, is determined for $n\\to\\infty$ and $p>0$. Then, it is applied to the calculation of the R\\'enyi entropy of the quantum-mechanical probability density of the highly-excited (Rydberg) states of the isotropic oscillator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3071","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":"2026-05-18T03:25:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r5gmkLo/cEGU6qJMSHSmDxEY/f0uYuvNmXqvCXn6XfbRef5ZPWkBSQElpcqlRsy3u5n++6jaKTppXQeIWPORAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T21:35:35.649863Z"},"content_sha256":"118ec06965215f606f9213e71e8c915ceb3e214a2c8f0ffbd13b0774a80689d5","schema_version":"1.0","event_id":"sha256:118ec06965215f606f9213e71e8c915ceb3e214a2c8f0ffbd13b0774a80689d5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TB34NZSDKIQDKI5EA2XLZZYVAI/bundle.json","state_url":"https://pith.science/pith/TB34NZSDKIQDKI5EA2XLZZYVAI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TB34NZSDKIQDKI5EA2XLZZYVAI/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":"2026-06-26T21:35:35Z","links":{"resolver":"https://pith.science/pith/TB34NZSDKIQDKI5EA2XLZZYVAI","bundle":"https://pith.science/pith/TB34NZSDKIQDKI5EA2XLZZYVAI/bundle.json","state":"https://pith.science/pith/TB34NZSDKIQDKI5EA2XLZZYVAI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TB34NZSDKIQDKI5EA2XLZZYVAI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TB34NZSDKIQDKI5EA2XLZZYVAI","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":"71331e0b1a80d58f438ce492ad0d6985759eaf5539de1ff05393ed6b0949b2bf","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-14T09:08:32Z","title_canon_sha256":"51d1c6d2dc2fbc0ab4881778a73356b7b185b6f501e0f299d0e180b6f51fb21d"},"schema_version":"1.0","source":{"id":"1305.3071","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.3071","created_at":"2026-05-18T03:25:44Z"},{"alias_kind":"arxiv_version","alias_value":"1305.3071v1","created_at":"2026-05-18T03:25:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3071","created_at":"2026-05-18T03:25:44Z"},{"alias_kind":"pith_short_12","alias_value":"TB34NZSDKIQD","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"TB34NZSDKIQDKI5E","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"TB34NZSD","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:118ec06965215f606f9213e71e8c915ceb3e214a2c8f0ffbd13b0774a80689d5","target":"graph","created_at":"2026-05-18T03:25:44Z","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 asymptotics of the weighted $L_{p}$-norms of Hermite polynomials, which describes the R\\'enyi entropy of order $p$ of the associated quantum oscillator probability density, is determined for $n\\to\\infty$ and $p>0$. Then, it is applied to the calculation of the R\\'enyi entropy of the quantum-mechanical probability density of the highly-excited (Rydberg) states of the isotropic oscillator.","authors_text":"Alexander I. Aptekarev, Dmitrii N. Tulyakov, Jes\\'us S. Dehesa, Pablo S\\'anchez-Moreno","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-14T09:08:32Z","title":"Asymptotics of $L_p$-norms of Hermite polynomials and R\\'enyi entropy of Rydberg oscillator states"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3071","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:ba5f1ffee08d9503ad2593401b2ee50a3064f0b0ab2e1a9321f04837a728f363","target":"record","created_at":"2026-05-18T03:25:44Z","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":"71331e0b1a80d58f438ce492ad0d6985759eaf5539de1ff05393ed6b0949b2bf","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-14T09:08:32Z","title_canon_sha256":"51d1c6d2dc2fbc0ab4881778a73356b7b185b6f501e0f299d0e180b6f51fb21d"},"schema_version":"1.0","source":{"id":"1305.3071","kind":"arxiv","version":1}},"canonical_sha256":"9877c6e64352203523a406aebce715020d5b07ab8f69bce6e627ae21601edad6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9877c6e64352203523a406aebce715020d5b07ab8f69bce6e627ae21601edad6","first_computed_at":"2026-05-18T03:25:44.934380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:44.934380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"06bcFcMHns0MK5pUXAkcopcH+xX2efP4iSVlkSAEyzTuwxVR2m1RfTH3JtEmtrBdCLfyhmDf3087cZDsgym4Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:44.935220Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.3071","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba5f1ffee08d9503ad2593401b2ee50a3064f0b0ab2e1a9321f04837a728f363","sha256:118ec06965215f606f9213e71e8c915ceb3e214a2c8f0ffbd13b0774a80689d5"],"state_sha256":"5e1133c1019e105d5731fac0e5c56cb3e0274edc6f44ffcc5b7d12b918a201dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JGuMzHN/TBsyXO7FCLAi+IN0fVKJyRSa40PTqHwUELL1h6l00Oaj9H+fAZaYm+DN6naD3Fv35bTIPPr52LF9Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T21:35:35.651926Z","bundle_sha256":"42824cf44ea9088cf96db8c6d5dad22a9228762ee58f9b52b213bbe67e713e2b"}}