{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:V4Y73VNZ2BPIS35FIRYMGGAVVW","short_pith_number":"pith:V4Y73VNZ","canonical_record":{"source":{"id":"0912.3890","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-12-19T12:38:49Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"c0b26634b3a3aead28bbb946d7ea8572459a8dffead695a7b9495a0015bedc46","abstract_canon_sha256":"f8615a711ed51e9fbb6a1871984475b5603b6f659d7478a9a59e6c09703bea09"},"schema_version":"1.0"},"canonical_sha256":"af31fdd5b9d05e896fa54470c31815adbd1aa8c44eea1fd5349ff565c6064083","source":{"kind":"arxiv","id":"0912.3890","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.3890","created_at":"2026-05-18T02:10:15Z"},{"alias_kind":"arxiv_version","alias_value":"0912.3890v2","created_at":"2026-05-18T02:10:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.3890","created_at":"2026-05-18T02:10:15Z"},{"alias_kind":"pith_short_12","alias_value":"V4Y73VNZ2BPI","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"V4Y73VNZ2BPIS35F","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"V4Y73VNZ","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:V4Y73VNZ2BPIS35FIRYMGGAVVW","target":"record","payload":{"canonical_record":{"source":{"id":"0912.3890","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-12-19T12:38:49Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"c0b26634b3a3aead28bbb946d7ea8572459a8dffead695a7b9495a0015bedc46","abstract_canon_sha256":"f8615a711ed51e9fbb6a1871984475b5603b6f659d7478a9a59e6c09703bea09"},"schema_version":"1.0"},"canonical_sha256":"af31fdd5b9d05e896fa54470c31815adbd1aa8c44eea1fd5349ff565c6064083","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:10:15.347427Z","signature_b64":"4KHR+5QbWRNgyeBNGBE5C70oRfz77+lNnDlKZYROf27cuyr5XMkXavCwx4jbr6kjzlNELgqwaZxg2nT/mUfmBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af31fdd5b9d05e896fa54470c31815adbd1aa8c44eea1fd5349ff565c6064083","last_reissued_at":"2026-05-18T02:10:15.346765Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:10:15.346765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0912.3890","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":"2026-05-18T02:10:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"65ckwPjzDSISRt+vFuiQnbWc+uudpvDRZxHH/aL4DnRsZmTPFXve0ILqJCBycjKWiS3zPMNavn+/H40uVN6tBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:02:23.871756Z"},"content_sha256":"92d48b6e060a1e803cbc80f9103105c6f0cd3006cdffc8e2276ff9ce10ccff9e","schema_version":"1.0","event_id":"sha256:92d48b6e060a1e803cbc80f9103105c6f0cd3006cdffc8e2276ff9ce10ccff9e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:V4Y73VNZ2BPIS35FIRYMGGAVVW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Any l-state analytical solutions of the Klein-Gordon equation for the Woods-Saxon potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"H.I.Ahmadov, S.V.Badalov, V.H.Badalov","submitted_at":"2009-12-19T12:38:49Z","abstract_excerpt":"The radial part of the Klein-Gordon equation for the Woods-Saxon potential is solved. In our calculations, we have applied the Nikiforov-Uvarov method by using the Pekeris approximation to the centrifugal potential for any $l$ states. The exact bound state energy eigenvalues and the corresponding eigenfunctions are obtained on the various values of the quantum numbers $n$ and $l$. The non-relativistic limit of the bound state energy spectrum was also found."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.3890","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":"2026-05-18T02:10:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9pUD7kP8cJBoWVjSQ6eLbAOPomJfekUbm0NWFaN96kMJ5yX8jj9jw2p2zPgrl82agex65N17Rmub/AS/CiP1Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:02:23.872492Z"},"content_sha256":"550ae30fe65dee920a3220394f9f3663da02d549bef52da9f4c26919d35f5c3e","schema_version":"1.0","event_id":"sha256:550ae30fe65dee920a3220394f9f3663da02d549bef52da9f4c26919d35f5c3e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V4Y73VNZ2BPIS35FIRYMGGAVVW/bundle.json","state_url":"https://pith.science/pith/V4Y73VNZ2BPIS35FIRYMGGAVVW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V4Y73VNZ2BPIS35FIRYMGGAVVW/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":"2026-06-04T17:02:23Z","links":{"resolver":"https://pith.science/pith/V4Y73VNZ2BPIS35FIRYMGGAVVW","bundle":"https://pith.science/pith/V4Y73VNZ2BPIS35FIRYMGGAVVW/bundle.json","state":"https://pith.science/pith/V4Y73VNZ2BPIS35FIRYMGGAVVW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V4Y73VNZ2BPIS35FIRYMGGAVVW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:V4Y73VNZ2BPIS35FIRYMGGAVVW","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":"f8615a711ed51e9fbb6a1871984475b5603b6f659d7478a9a59e6c09703bea09","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-12-19T12:38:49Z","title_canon_sha256":"c0b26634b3a3aead28bbb946d7ea8572459a8dffead695a7b9495a0015bedc46"},"schema_version":"1.0","source":{"id":"0912.3890","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.3890","created_at":"2026-05-18T02:10:15Z"},{"alias_kind":"arxiv_version","alias_value":"0912.3890v2","created_at":"2026-05-18T02:10:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.3890","created_at":"2026-05-18T02:10:15Z"},{"alias_kind":"pith_short_12","alias_value":"V4Y73VNZ2BPI","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"V4Y73VNZ2BPIS35F","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"V4Y73VNZ","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:550ae30fe65dee920a3220394f9f3663da02d549bef52da9f4c26919d35f5c3e","target":"graph","created_at":"2026-05-18T02:10:15Z","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 radial part of the Klein-Gordon equation for the Woods-Saxon potential is solved. In our calculations, we have applied the Nikiforov-Uvarov method by using the Pekeris approximation to the centrifugal potential for any $l$ states. The exact bound state energy eigenvalues and the corresponding eigenfunctions are obtained on the various values of the quantum numbers $n$ and $l$. The non-relativistic limit of the bound state energy spectrum was also found.","authors_text":"H.I.Ahmadov, S.V.Badalov, V.H.Badalov","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-12-19T12:38:49Z","title":"Any l-state analytical solutions of the Klein-Gordon equation for the Woods-Saxon potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.3890","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":"sha256:92d48b6e060a1e803cbc80f9103105c6f0cd3006cdffc8e2276ff9ce10ccff9e","target":"record","created_at":"2026-05-18T02:10:15Z","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":"f8615a711ed51e9fbb6a1871984475b5603b6f659d7478a9a59e6c09703bea09","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-12-19T12:38:49Z","title_canon_sha256":"c0b26634b3a3aead28bbb946d7ea8572459a8dffead695a7b9495a0015bedc46"},"schema_version":"1.0","source":{"id":"0912.3890","kind":"arxiv","version":2}},"canonical_sha256":"af31fdd5b9d05e896fa54470c31815adbd1aa8c44eea1fd5349ff565c6064083","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af31fdd5b9d05e896fa54470c31815adbd1aa8c44eea1fd5349ff565c6064083","first_computed_at":"2026-05-18T02:10:15.346765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:10:15.346765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4KHR+5QbWRNgyeBNGBE5C70oRfz77+lNnDlKZYROf27cuyr5XMkXavCwx4jbr6kjzlNELgqwaZxg2nT/mUfmBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:10:15.347427Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.3890","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92d48b6e060a1e803cbc80f9103105c6f0cd3006cdffc8e2276ff9ce10ccff9e","sha256:550ae30fe65dee920a3220394f9f3663da02d549bef52da9f4c26919d35f5c3e"],"state_sha256":"215e3c1483dd915d16fbc7fc5d720deb1a6a4fc47dde461ce48cdf7edbd625c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6PTb0a6AVd9lJmkFDnwGP5siCJmk/YPypG/ypWRX1vWXV4ygdFtfpEQx7FHtPKquY2+35K/V221fwn/6ksOtAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T17:02:23.875523Z","bundle_sha256":"ef02bb8ceddb9abd66ac24d403121ecc0b8e4006a64017726d2fa75c4496b1c8"}}