{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:TS7ALPWBZPL55DGPA7AXPBSAMX","short_pith_number":"pith:TS7ALPWB","canonical_record":{"source":{"id":"1210.4205","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-15T21:56:07Z","cross_cats_sorted":[],"title_canon_sha256":"1c32c070663595f5735ba834c1c44a4505847819010b217809841591159ae51c","abstract_canon_sha256":"50dd773b31970c021cc3242607b27305488a2daa6069511abedf5864fd86cf62"},"schema_version":"1.0"},"canonical_sha256":"9cbe05bec1cbd7de8ccf07c177864065fb59aaf7fe5b297550170736bc03d066","source":{"kind":"arxiv","id":"1210.4205","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4205","created_at":"2026-05-18T03:21:54Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4205v2","created_at":"2026-05-18T03:21:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4205","created_at":"2026-05-18T03:21:54Z"},{"alias_kind":"pith_short_12","alias_value":"TS7ALPWBZPL5","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TS7ALPWBZPL55DGP","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TS7ALPWB","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:TS7ALPWBZPL55DGPA7AXPBSAMX","target":"record","payload":{"canonical_record":{"source":{"id":"1210.4205","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-15T21:56:07Z","cross_cats_sorted":[],"title_canon_sha256":"1c32c070663595f5735ba834c1c44a4505847819010b217809841591159ae51c","abstract_canon_sha256":"50dd773b31970c021cc3242607b27305488a2daa6069511abedf5864fd86cf62"},"schema_version":"1.0"},"canonical_sha256":"9cbe05bec1cbd7de8ccf07c177864065fb59aaf7fe5b297550170736bc03d066","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:54.047121Z","signature_b64":"Sqmwv/omN5Ue72UKZnN1ZcpCrCwqQiZ/5KS40+I4dzSEbiQaqO1Almf14Io/I5lk2IezICSkSx/jvBcdJhDQDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9cbe05bec1cbd7de8ccf07c177864065fb59aaf7fe5b297550170736bc03d066","last_reissued_at":"2026-05-18T03:21:54.046674Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:54.046674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.4205","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:21:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vMa6oVXEj1sqIs12AYf0c7JuMB2gugBxj0dr1xxUHk3sWeQQxzkZM8G5FGwjVJb5ZVx/BqyFbzao14DpUc5FCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:17:07.272583Z"},"content_sha256":"db6fac0886465f7f01e8790e11789e8efd56833787e40e0331d7f1a9482f8ec2","schema_version":"1.0","event_id":"sha256:db6fac0886465f7f01e8790e11789e8efd56833787e40e0331d7f1a9482f8ec2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:TS7ALPWBZPL55DGPA7AXPBSAMX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local approximation to the critical parameters of quantum wells","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Francisco M. Fern\\'andez, Javier Garcia","submitted_at":"2012-10-15T21:56:07Z","abstract_excerpt":"We calculate the critical parameters for some simple quantum wells by means of the Riccati-Pad\\'{e} method. The original approach converges reasonably well for nonzero angular-momentum quantum number $l$ but rather too slowly for the s states. We therefore propose a simple modification that yields remarkably accurate results for the latter case. The rate of convergence of both methods increases with $l$ and decreases with the radial quantum number $n$. We compare RPM results with WKB ones for sufficiently large values of $l$. As illustrative examples we choose the one-dimensional and central-f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4205","kind":"arxiv","version":2},"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":"2026-05-18T03:21:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AY9jKBPN77ZzWlmEx3PsLc14oFo6rMV+mdnh3V7T9wCqi82lJCylN4PNFZXCgLk1PHWMIAj9WiTeCQdx3ab7Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:17:07.272934Z"},"content_sha256":"875b9c1cfbb7154face6a4fe2d621bf2f3d264b0961e4d7e85092a146072a1c1","schema_version":"1.0","event_id":"sha256:875b9c1cfbb7154face6a4fe2d621bf2f3d264b0961e4d7e85092a146072a1c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TS7ALPWBZPL55DGPA7AXPBSAMX/bundle.json","state_url":"https://pith.science/pith/TS7ALPWBZPL55DGPA7AXPBSAMX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TS7ALPWBZPL55DGPA7AXPBSAMX/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":"2026-05-25T12:17:07Z","links":{"resolver":"https://pith.science/pith/TS7ALPWBZPL55DGPA7AXPBSAMX","bundle":"https://pith.science/pith/TS7ALPWBZPL55DGPA7AXPBSAMX/bundle.json","state":"https://pith.science/pith/TS7ALPWBZPL55DGPA7AXPBSAMX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TS7ALPWBZPL55DGPA7AXPBSAMX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TS7ALPWBZPL55DGPA7AXPBSAMX","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":"50dd773b31970c021cc3242607b27305488a2daa6069511abedf5864fd86cf62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-15T21:56:07Z","title_canon_sha256":"1c32c070663595f5735ba834c1c44a4505847819010b217809841591159ae51c"},"schema_version":"1.0","source":{"id":"1210.4205","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4205","created_at":"2026-05-18T03:21:54Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4205v2","created_at":"2026-05-18T03:21:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4205","created_at":"2026-05-18T03:21:54Z"},{"alias_kind":"pith_short_12","alias_value":"TS7ALPWBZPL5","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TS7ALPWBZPL55DGP","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TS7ALPWB","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:875b9c1cfbb7154face6a4fe2d621bf2f3d264b0961e4d7e85092a146072a1c1","target":"graph","created_at":"2026-05-18T03:21:54Z","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 calculate the critical parameters for some simple quantum wells by means of the Riccati-Pad\\'{e} method. The original approach converges reasonably well for nonzero angular-momentum quantum number $l$ but rather too slowly for the s states. We therefore propose a simple modification that yields remarkably accurate results for the latter case. The rate of convergence of both methods increases with $l$ and decreases with the radial quantum number $n$. We compare RPM results with WKB ones for sufficiently large values of $l$. As illustrative examples we choose the one-dimensional and central-f","authors_text":"Francisco M. Fern\\'andez, Javier Garcia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-15T21:56:07Z","title":"Local approximation to the critical parameters of quantum wells"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4205","kind":"arxiv","version":2},"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:db6fac0886465f7f01e8790e11789e8efd56833787e40e0331d7f1a9482f8ec2","target":"record","created_at":"2026-05-18T03:21:54Z","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":"50dd773b31970c021cc3242607b27305488a2daa6069511abedf5864fd86cf62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-15T21:56:07Z","title_canon_sha256":"1c32c070663595f5735ba834c1c44a4505847819010b217809841591159ae51c"},"schema_version":"1.0","source":{"id":"1210.4205","kind":"arxiv","version":2}},"canonical_sha256":"9cbe05bec1cbd7de8ccf07c177864065fb59aaf7fe5b297550170736bc03d066","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9cbe05bec1cbd7de8ccf07c177864065fb59aaf7fe5b297550170736bc03d066","first_computed_at":"2026-05-18T03:21:54.046674Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:54.046674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Sqmwv/omN5Ue72UKZnN1ZcpCrCwqQiZ/5KS40+I4dzSEbiQaqO1Almf14Io/I5lk2IezICSkSx/jvBcdJhDQDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:54.047121Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.4205","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db6fac0886465f7f01e8790e11789e8efd56833787e40e0331d7f1a9482f8ec2","sha256:875b9c1cfbb7154face6a4fe2d621bf2f3d264b0961e4d7e85092a146072a1c1"],"state_sha256":"3de7e3585b33861fd3eaa8b993d3153de690a7c81274565243ae1eeb08ec0446"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hs/lQns8fdOhYp92G/u23ZiSq8rfdYy9LxisaAzbTyxUnhA2lRkJgkFwxEUaqt7sIBMacQGkYjO6v+B8HemyCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T12:17:07.275505Z","bundle_sha256":"d550c5c682e4b7daeff2564ff473afb8502f0c489df15717cc3aff60c0f0b492"}}