{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:KZ6BIUSIJB5WP73XWPNSEYKIAI","short_pith_number":"pith:KZ6BIUSI","canonical_record":{"source":{"id":"2209.14332","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-09-28T18:02:58Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"21f4f972c6c4cfbbc42567eb63fa6cabe16450e4cfd4929394808e83c3d7fc5e","abstract_canon_sha256":"13c579cd287d18e2ec47d67b738ff2544361d2244b29e78f0208d889f417bd99"},"schema_version":"1.0"},"canonical_sha256":"567c145248487b67ff77b3db22614802110d3ed07a9cc983821b411affaa7a5e","source":{"kind":"arxiv","id":"2209.14332","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.14332","created_at":"2026-07-05T06:18:09Z"},{"alias_kind":"arxiv_version","alias_value":"2209.14332v1","created_at":"2026-07-05T06:18:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.14332","created_at":"2026-07-05T06:18:09Z"},{"alias_kind":"pith_short_12","alias_value":"KZ6BIUSIJB5W","created_at":"2026-07-05T06:18:09Z"},{"alias_kind":"pith_short_16","alias_value":"KZ6BIUSIJB5WP73X","created_at":"2026-07-05T06:18:09Z"},{"alias_kind":"pith_short_8","alias_value":"KZ6BIUSI","created_at":"2026-07-05T06:18:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:KZ6BIUSIJB5WP73XWPNSEYKIAI","target":"record","payload":{"canonical_record":{"source":{"id":"2209.14332","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-09-28T18:02:58Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"21f4f972c6c4cfbbc42567eb63fa6cabe16450e4cfd4929394808e83c3d7fc5e","abstract_canon_sha256":"13c579cd287d18e2ec47d67b738ff2544361d2244b29e78f0208d889f417bd99"},"schema_version":"1.0"},"canonical_sha256":"567c145248487b67ff77b3db22614802110d3ed07a9cc983821b411affaa7a5e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:18:09.266247Z","signature_b64":"HqPwJfs/xEVQDobXRnR78VtmA6rtL70N2wwazSWcIx3YGpFkK6pMtq+PnJHDqLn2RisQgu4xgFcMV2FJNt0YCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"567c145248487b67ff77b3db22614802110d3ed07a9cc983821b411affaa7a5e","last_reissued_at":"2026-07-05T06:18:09.265664Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:18:09.265664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.14332","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":"2026-07-05T06:18:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cjEl3DcuEelIK9vwZRoGt8+IU4RZ20UFc/WtN3s59fpp1sSxZJCpONQEjjqfIhZgRJBQnczrxLr4UyRvW8DHAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T09:28:10.400800Z"},"content_sha256":"477009487622d3977851837efa0b6cf80117dcea87493154d629d706e6c4c6c9","schema_version":"1.0","event_id":"sha256:477009487622d3977851837efa0b6cf80117dcea87493154d629d706e6c4c6c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:KZ6BIUSIJB5WP73XWPNSEYKIAI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Semidefinite Programming algorithm for the Quantum Mechanical Bootstrap","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"hep-th","authors_text":"David Berenstein, George Hulsey","submitted_at":"2022-09-28T18:02:58Z","abstract_excerpt":"We present a semidefinite program (SDP) algorithm to find eigenvalues of Schr\\\"{o}dinger operators within the bootstrap approach to quantum mechanics. The bootstrap approach involves two ingredients: a nonlinear set of constraints on the variables (expectation values of operators in an energy eigenstate), plus positivity constraints (unitarity) that need to be satisfied. By fixing the energy we linearize all the constraints and show that the feasability problem can be presented as an optimization problem for the variables that are not fixed by the constraints and one additional slack variable "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.14332","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.14332/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T06:18:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jESp73BNJlSGsQXCpqJ2huS6OKZ4SIw2rUtxhg9RokJ6FS7IfX965jG2tdiMLzC4diIu4mqkBqYrTWorWRyzCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T09:28:10.401679Z"},"content_sha256":"5bb7527f9c38fab4fea431b1f66a4ebc43275bc12d1a0067184f401affa9089b","schema_version":"1.0","event_id":"sha256:5bb7527f9c38fab4fea431b1f66a4ebc43275bc12d1a0067184f401affa9089b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KZ6BIUSIJB5WP73XWPNSEYKIAI/bundle.json","state_url":"https://pith.science/pith/KZ6BIUSIJB5WP73XWPNSEYKIAI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KZ6BIUSIJB5WP73XWPNSEYKIAI/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":"2026-08-17T09:28:10Z","links":{"resolver":"https://pith.science/pith/KZ6BIUSIJB5WP73XWPNSEYKIAI","bundle":"https://pith.science/pith/KZ6BIUSIJB5WP73XWPNSEYKIAI/bundle.json","state":"https://pith.science/pith/KZ6BIUSIJB5WP73XWPNSEYKIAI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KZ6BIUSIJB5WP73XWPNSEYKIAI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:KZ6BIUSIJB5WP73XWPNSEYKIAI","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":"13c579cd287d18e2ec47d67b738ff2544361d2244b29e78f0208d889f417bd99","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-09-28T18:02:58Z","title_canon_sha256":"21f4f972c6c4cfbbc42567eb63fa6cabe16450e4cfd4929394808e83c3d7fc5e"},"schema_version":"1.0","source":{"id":"2209.14332","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.14332","created_at":"2026-07-05T06:18:09Z"},{"alias_kind":"arxiv_version","alias_value":"2209.14332v1","created_at":"2026-07-05T06:18:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.14332","created_at":"2026-07-05T06:18:09Z"},{"alias_kind":"pith_short_12","alias_value":"KZ6BIUSIJB5W","created_at":"2026-07-05T06:18:09Z"},{"alias_kind":"pith_short_16","alias_value":"KZ6BIUSIJB5WP73X","created_at":"2026-07-05T06:18:09Z"},{"alias_kind":"pith_short_8","alias_value":"KZ6BIUSI","created_at":"2026-07-05T06:18:09Z"}],"graph_snapshots":[{"event_id":"sha256:5bb7527f9c38fab4fea431b1f66a4ebc43275bc12d1a0067184f401affa9089b","target":"graph","created_at":"2026-07-05T06:18:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2209.14332/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a semidefinite program (SDP) algorithm to find eigenvalues of Schr\\\"{o}dinger operators within the bootstrap approach to quantum mechanics. The bootstrap approach involves two ingredients: a nonlinear set of constraints on the variables (expectation values of operators in an energy eigenstate), plus positivity constraints (unitarity) that need to be satisfied. By fixing the energy we linearize all the constraints and show that the feasability problem can be presented as an optimization problem for the variables that are not fixed by the constraints and one additional slack variable ","authors_text":"David Berenstein, George Hulsey","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-09-28T18:02:58Z","title":"A Semidefinite Programming algorithm for the Quantum Mechanical Bootstrap"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.14332","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":"sha256:477009487622d3977851837efa0b6cf80117dcea87493154d629d706e6c4c6c9","target":"record","created_at":"2026-07-05T06:18:09Z","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":"13c579cd287d18e2ec47d67b738ff2544361d2244b29e78f0208d889f417bd99","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-09-28T18:02:58Z","title_canon_sha256":"21f4f972c6c4cfbbc42567eb63fa6cabe16450e4cfd4929394808e83c3d7fc5e"},"schema_version":"1.0","source":{"id":"2209.14332","kind":"arxiv","version":1}},"canonical_sha256":"567c145248487b67ff77b3db22614802110d3ed07a9cc983821b411affaa7a5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"567c145248487b67ff77b3db22614802110d3ed07a9cc983821b411affaa7a5e","first_computed_at":"2026-07-05T06:18:09.265664Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:18:09.265664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HqPwJfs/xEVQDobXRnR78VtmA6rtL70N2wwazSWcIx3YGpFkK6pMtq+PnJHDqLn2RisQgu4xgFcMV2FJNt0YCw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:18:09.266247Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.14332","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:477009487622d3977851837efa0b6cf80117dcea87493154d629d706e6c4c6c9","sha256:5bb7527f9c38fab4fea431b1f66a4ebc43275bc12d1a0067184f401affa9089b"],"state_sha256":"ebdbb290a32f5db91a824fce28f5a2bbe8f560708128223bdf22c1bda80547c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jfOULPtbLS5euR+erIah9hnQcs/0gA1hQ7sfk6dScEntk/KzrkYtWUNDv1S0QI4DmNPMDYumoUGyR+5vOTBkAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T09:28:10.409204Z","bundle_sha256":"4fd17dff4ef2ad907446cde47368844236344d5e8cdbf71e0621050c3e1e027f"}}