{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:MZRF4B355N2ZNGV6DDIPSNUDWA","short_pith_number":"pith:MZRF4B35","canonical_record":{"source":{"id":"1305.4743","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-05-21T07:49:57Z","cross_cats_sorted":[],"title_canon_sha256":"b65ba7950001dba596baeb0dbc916fae90c865216047d995d21a9b774232f776","abstract_canon_sha256":"a87802dd363492856270201b1f4e8471a662b2a742cc39d3a0fcf8e456b290bb"},"schema_version":"1.0"},"canonical_sha256":"66625e077deb75969abe18d0f93683b01cd7178775ff49dfd5246c3ebce7ea5e","source":{"kind":"arxiv","id":"1305.4743","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.4743","created_at":"2026-05-18T03:25:15Z"},{"alias_kind":"arxiv_version","alias_value":"1305.4743v1","created_at":"2026-05-18T03:25:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.4743","created_at":"2026-05-18T03:25:15Z"},{"alias_kind":"pith_short_12","alias_value":"MZRF4B355N2Z","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MZRF4B355N2ZNGV6","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MZRF4B35","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:MZRF4B355N2ZNGV6DDIPSNUDWA","target":"record","payload":{"canonical_record":{"source":{"id":"1305.4743","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-05-21T07:49:57Z","cross_cats_sorted":[],"title_canon_sha256":"b65ba7950001dba596baeb0dbc916fae90c865216047d995d21a9b774232f776","abstract_canon_sha256":"a87802dd363492856270201b1f4e8471a662b2a742cc39d3a0fcf8e456b290bb"},"schema_version":"1.0"},"canonical_sha256":"66625e077deb75969abe18d0f93683b01cd7178775ff49dfd5246c3ebce7ea5e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:15.337778Z","signature_b64":"xlROh7Z3ZHWTvhAW93dHOCGTbXbm17T1p0XPYlA7mNc89pIs/FIAyI7G67l1IbqxM+p+hucoil2RmFPHrh4HBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66625e077deb75969abe18d0f93683b01cd7178775ff49dfd5246c3ebce7ea5e","last_reissued_at":"2026-05-18T03:25:15.337182Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:15.337182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.4743","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":"2026-05-18T03:25:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hfBrfV1W/6W8vFKYYAPJbR3+gnxXT/ln7GeBQD4cp7wk5QTTbrensGSh2OHz+XN9hu8hHTbhPYvmeUlg7RR+Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T21:36:22.335884Z"},"content_sha256":"c5b11ad2ac8413716d0776366a380353f1c6ee0b1d30b382252c8fdedd56692d","schema_version":"1.0","event_id":"sha256:c5b11ad2ac8413716d0776366a380353f1c6ee0b1d30b382252c8fdedd56692d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:MZRF4B355N2ZNGV6DDIPSNUDWA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Renyi entropy of the infinite well potential in momentum space and Dirichlet-like trigonometric functionals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Alexander I. Aptekarev, D.N. Tulyakov, Jesus S. Dehesa, Pablo S\\'anchez-Moreno","submitted_at":"2013-05-21T07:49:57Z","abstract_excerpt":"The momentum entropic moments and R\\'enyi entropies of a one-dimensional particle in an infinite well potential are found by means of explicit calculations of some Dirichlet-like trigonometric integrals. The associated spreading lengths and quantum uncertainty-like sums are also provided."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4743","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":"2026-05-18T03:25:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/q0YS/Qxq+XSlgk8qydN7ZNlB3r+84IRPZivKN9bz2743ne5IfQaFiNnmBqD5Hl3MaG8NfJalG2SwQsUSvFMDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T21:36:22.336227Z"},"content_sha256":"d50229b760ad1c87179d797c192adfab6a784471da4556afa433aab7a3cb175d","schema_version":"1.0","event_id":"sha256:d50229b760ad1c87179d797c192adfab6a784471da4556afa433aab7a3cb175d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MZRF4B355N2ZNGV6DDIPSNUDWA/bundle.json","state_url":"https://pith.science/pith/MZRF4B355N2ZNGV6DDIPSNUDWA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MZRF4B355N2ZNGV6DDIPSNUDWA/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":"2026-06-20T21:36:22Z","links":{"resolver":"https://pith.science/pith/MZRF4B355N2ZNGV6DDIPSNUDWA","bundle":"https://pith.science/pith/MZRF4B355N2ZNGV6DDIPSNUDWA/bundle.json","state":"https://pith.science/pith/MZRF4B355N2ZNGV6DDIPSNUDWA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MZRF4B355N2ZNGV6DDIPSNUDWA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MZRF4B355N2ZNGV6DDIPSNUDWA","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":"a87802dd363492856270201b1f4e8471a662b2a742cc39d3a0fcf8e456b290bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-05-21T07:49:57Z","title_canon_sha256":"b65ba7950001dba596baeb0dbc916fae90c865216047d995d21a9b774232f776"},"schema_version":"1.0","source":{"id":"1305.4743","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.4743","created_at":"2026-05-18T03:25:15Z"},{"alias_kind":"arxiv_version","alias_value":"1305.4743v1","created_at":"2026-05-18T03:25:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.4743","created_at":"2026-05-18T03:25:15Z"},{"alias_kind":"pith_short_12","alias_value":"MZRF4B355N2Z","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MZRF4B355N2ZNGV6","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MZRF4B35","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:d50229b760ad1c87179d797c192adfab6a784471da4556afa433aab7a3cb175d","target":"graph","created_at":"2026-05-18T03:25:15Z","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 momentum entropic moments and R\\'enyi entropies of a one-dimensional particle in an infinite well potential are found by means of explicit calculations of some Dirichlet-like trigonometric integrals. The associated spreading lengths and quantum uncertainty-like sums are also provided.","authors_text":"Alexander I. Aptekarev, D.N. Tulyakov, Jesus S. Dehesa, Pablo S\\'anchez-Moreno","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-05-21T07:49:57Z","title":"Renyi entropy of the infinite well potential in momentum space and Dirichlet-like trigonometric functionals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4743","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:c5b11ad2ac8413716d0776366a380353f1c6ee0b1d30b382252c8fdedd56692d","target":"record","created_at":"2026-05-18T03:25:15Z","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":"a87802dd363492856270201b1f4e8471a662b2a742cc39d3a0fcf8e456b290bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-05-21T07:49:57Z","title_canon_sha256":"b65ba7950001dba596baeb0dbc916fae90c865216047d995d21a9b774232f776"},"schema_version":"1.0","source":{"id":"1305.4743","kind":"arxiv","version":1}},"canonical_sha256":"66625e077deb75969abe18d0f93683b01cd7178775ff49dfd5246c3ebce7ea5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66625e077deb75969abe18d0f93683b01cd7178775ff49dfd5246c3ebce7ea5e","first_computed_at":"2026-05-18T03:25:15.337182Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:15.337182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xlROh7Z3ZHWTvhAW93dHOCGTbXbm17T1p0XPYlA7mNc89pIs/FIAyI7G67l1IbqxM+p+hucoil2RmFPHrh4HBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:15.337778Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.4743","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5b11ad2ac8413716d0776366a380353f1c6ee0b1d30b382252c8fdedd56692d","sha256:d50229b760ad1c87179d797c192adfab6a784471da4556afa433aab7a3cb175d"],"state_sha256":"19c9807efe2d28e20eaba74080ef3fb177d78e894cbfa1b1eda0808597a78dea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4kCboqxWFRvf12xX+xTB1KJbqUMY9hIDv1F8L2HSGBVHZQXIcHSt/WDgiTifieWC5G13e+s72nEQbP4akyZMBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T21:36:22.338242Z","bundle_sha256":"1142bcd36834ba6495986438dae7ba59ea45c14dfb77a1c234f99b0a6c04b6e3"}}