{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ADD6YWOWWFQWFJIJYTJEWLTXZW","short_pith_number":"pith:ADD6YWOW","canonical_record":{"source":{"id":"1102.5356","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-02-25T21:45:22Z","cross_cats_sorted":["cond-mat.other","hep-th","math.MP","math.NT","quant-ph"],"title_canon_sha256":"46de9ae54269619aa9664983c01ec0c09e96254ef328d09247a6f506cb1a20d6","abstract_canon_sha256":"d0f9ea9b2140f609868817b1051f49d30822e3e94fceae4dfdcf599835b877aa"},"schema_version":"1.0"},"canonical_sha256":"00c7ec59d6b16162a509c4d24b2e77cdb7fdd6606b6ad878eeaa9d10592a37ab","source":{"kind":"arxiv","id":"1102.5356","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.5356","created_at":"2026-05-18T04:21:50Z"},{"alias_kind":"arxiv_version","alias_value":"1102.5356v1","created_at":"2026-05-18T04:21:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.5356","created_at":"2026-05-18T04:21:50Z"},{"alias_kind":"pith_short_12","alias_value":"ADD6YWOWWFQW","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"ADD6YWOWWFQWFJIJ","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"ADD6YWOW","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ADD6YWOWWFQWFJIJYTJEWLTXZW","target":"record","payload":{"canonical_record":{"source":{"id":"1102.5356","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-02-25T21:45:22Z","cross_cats_sorted":["cond-mat.other","hep-th","math.MP","math.NT","quant-ph"],"title_canon_sha256":"46de9ae54269619aa9664983c01ec0c09e96254ef328d09247a6f506cb1a20d6","abstract_canon_sha256":"d0f9ea9b2140f609868817b1051f49d30822e3e94fceae4dfdcf599835b877aa"},"schema_version":"1.0"},"canonical_sha256":"00c7ec59d6b16162a509c4d24b2e77cdb7fdd6606b6ad878eeaa9d10592a37ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:50.407348Z","signature_b64":"m96fuS6zVrxpOuMLd4BpVu6R559nHIdFT+SnGPeDPO4kiGrvP5XJbtyEMsKlj6Y/SAdpQjdrfr5/OZ1QdsAOCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00c7ec59d6b16162a509c4d24b2e77cdb7fdd6606b6ad878eeaa9d10592a37ab","last_reissued_at":"2026-05-18T04:21:50.406887Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:50.406887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.5356","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":"2026-05-18T04:21:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rNBEf+9zufzdYbBHyx4j0O1ReojWuDkYlz6YkSq+IiV3oqPFk7sfcfz4p8KaXEeg9kYmwDj3rv9YljwRaBYoAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:08:08.072278Z"},"content_sha256":"d9359ca85a11f8ff583bfc4157a624fb71addcb6e27ae90087cb83419b0090f7","schema_version":"1.0","event_id":"sha256:d9359ca85a11f8ff583bfc4157a624fb71addcb6e27ae90087cb83419b0090f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ADD6YWOWWFQWFJIJYTJEWLTXZW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The H=xp model revisited and the Riemann zeros","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.other","hep-th","math.MP","math.NT","quant-ph"],"primary_cat":"math-ph","authors_text":"German Sierra, Javier Rodriguez-Laguna","submitted_at":"2011-02-25T21:45:22Z","abstract_excerpt":"Berry and Keating conjectured that the classical Hamiltonian H = xp is related to the Riemann zeros. A regularization of this model yields semiclassical energies that behave, in average, as the non trivial zeros of the Riemann zeta function. However, the classical trajectories are not closed, rendering the model incomplete. In this paper, we show that the Hamiltonian H = x (p + l_p^2/p) contains closed periodic orbits, and that its spectrum coincides with the average Riemann zeros. This result is generalized to Dirichlet L-functions using different self-adjoint extensions of H. We discuss the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5356","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":"2026-05-18T04:21:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GV5hhFmxSDawf2LinK1ZTe1CXq0IGaNfJCzcjBKSu2KMbLVbbIe9pUzgDrlXBTUk0d3XEUN2w74Wd7jbiNMtDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:08:08.073011Z"},"content_sha256":"e5c702f2c10f7e3b7dedfc7777d84a4bd5c7fa236d7608f948f2ee02fa7a21ee","schema_version":"1.0","event_id":"sha256:e5c702f2c10f7e3b7dedfc7777d84a4bd5c7fa236d7608f948f2ee02fa7a21ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ADD6YWOWWFQWFJIJYTJEWLTXZW/bundle.json","state_url":"https://pith.science/pith/ADD6YWOWWFQWFJIJYTJEWLTXZW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ADD6YWOWWFQWFJIJYTJEWLTXZW/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":"2026-06-09T12:08:08Z","links":{"resolver":"https://pith.science/pith/ADD6YWOWWFQWFJIJYTJEWLTXZW","bundle":"https://pith.science/pith/ADD6YWOWWFQWFJIJYTJEWLTXZW/bundle.json","state":"https://pith.science/pith/ADD6YWOWWFQWFJIJYTJEWLTXZW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ADD6YWOWWFQWFJIJYTJEWLTXZW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ADD6YWOWWFQWFJIJYTJEWLTXZW","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":"d0f9ea9b2140f609868817b1051f49d30822e3e94fceae4dfdcf599835b877aa","cross_cats_sorted":["cond-mat.other","hep-th","math.MP","math.NT","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-02-25T21:45:22Z","title_canon_sha256":"46de9ae54269619aa9664983c01ec0c09e96254ef328d09247a6f506cb1a20d6"},"schema_version":"1.0","source":{"id":"1102.5356","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.5356","created_at":"2026-05-18T04:21:50Z"},{"alias_kind":"arxiv_version","alias_value":"1102.5356v1","created_at":"2026-05-18T04:21:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.5356","created_at":"2026-05-18T04:21:50Z"},{"alias_kind":"pith_short_12","alias_value":"ADD6YWOWWFQW","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"ADD6YWOWWFQWFJIJ","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"ADD6YWOW","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:e5c702f2c10f7e3b7dedfc7777d84a4bd5c7fa236d7608f948f2ee02fa7a21ee","target":"graph","created_at":"2026-05-18T04:21:50Z","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":"Berry and Keating conjectured that the classical Hamiltonian H = xp is related to the Riemann zeros. A regularization of this model yields semiclassical energies that behave, in average, as the non trivial zeros of the Riemann zeta function. However, the classical trajectories are not closed, rendering the model incomplete. In this paper, we show that the Hamiltonian H = x (p + l_p^2/p) contains closed periodic orbits, and that its spectrum coincides with the average Riemann zeros. This result is generalized to Dirichlet L-functions using different self-adjoint extensions of H. We discuss the ","authors_text":"German Sierra, Javier Rodriguez-Laguna","cross_cats":["cond-mat.other","hep-th","math.MP","math.NT","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-02-25T21:45:22Z","title":"The H=xp model revisited and the Riemann zeros"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5356","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:d9359ca85a11f8ff583bfc4157a624fb71addcb6e27ae90087cb83419b0090f7","target":"record","created_at":"2026-05-18T04:21:50Z","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":"d0f9ea9b2140f609868817b1051f49d30822e3e94fceae4dfdcf599835b877aa","cross_cats_sorted":["cond-mat.other","hep-th","math.MP","math.NT","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-02-25T21:45:22Z","title_canon_sha256":"46de9ae54269619aa9664983c01ec0c09e96254ef328d09247a6f506cb1a20d6"},"schema_version":"1.0","source":{"id":"1102.5356","kind":"arxiv","version":1}},"canonical_sha256":"00c7ec59d6b16162a509c4d24b2e77cdb7fdd6606b6ad878eeaa9d10592a37ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00c7ec59d6b16162a509c4d24b2e77cdb7fdd6606b6ad878eeaa9d10592a37ab","first_computed_at":"2026-05-18T04:21:50.406887Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:50.406887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m96fuS6zVrxpOuMLd4BpVu6R559nHIdFT+SnGPeDPO4kiGrvP5XJbtyEMsKlj6Y/SAdpQjdrfr5/OZ1QdsAOCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:50.407348Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.5356","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9359ca85a11f8ff583bfc4157a624fb71addcb6e27ae90087cb83419b0090f7","sha256:e5c702f2c10f7e3b7dedfc7777d84a4bd5c7fa236d7608f948f2ee02fa7a21ee"],"state_sha256":"537fe7499e15ee7f61b1e17f1208cff203ae88621cb48e9b86faea7ad0622205"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LbPAHPNISEOrg9qTExSTYVd2OKQeMS1igNVmgobKL7v1n58pBcg6mnFet52HWooWy5rBsi5K0YGIsgpJpO19Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T12:08:08.077281Z","bundle_sha256":"61053843e3504a8131321bb3d0fabb263eba2149c3e3ded05cacf8acdadd636e"}}