{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:KEU2TJ7FFID3DZTQDIWXGPA7IS","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":"69287ae23b3aef241aa7f6d5ad3f876ce1981b201d0545fca62c2bdfa5a52c1c","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2008-11-19T10:18:19Z","title_canon_sha256":"a8e269f96ab20814cef8ef65ce0c903b26d994b91a9447d23f046d35e58539c8"},"schema_version":"1.0","source":{"id":"0811.3073","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.3073","created_at":"2026-05-18T02:15:14Z"},{"alias_kind":"arxiv_version","alias_value":"0811.3073v2","created_at":"2026-05-18T02:15:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.3073","created_at":"2026-05-18T02:15:14Z"},{"alias_kind":"pith_short_12","alias_value":"KEU2TJ7FFID3","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"KEU2TJ7FFID3DZTQ","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"KEU2TJ7F","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:b3f5e89fde02fd39a05aecb9c4d9227a2b1445f0c830a9c2737efd89905222f0","target":"graph","created_at":"2026-05-18T02:15:14Z","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 first step in the counting operator analysis of the spectrum of any model Hamiltonian H is the choice of a Hermitean operator M in such a way that the third commutator with H is proportional to the first commutator. Next one calculates operators R and R^\\dagger which share some of the properties of creation and annihilation operators, and such that $M$ becomes a counting operator. The spectrum of H is then decomposed into multiplets, not determined by the symmetries of H, but by those of a reference Hamiltonian H_ref, which is defined by H_ref=H-R-R^\\dagger, and which commutes with M. Fina","authors_text":"Ben Anthonis, Jan Naudts, Tobias Verhulst","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2008-11-19T10:18:19Z","title":"Counting operator analysis of the discrete spectrum of some model Hamiltonians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.3073","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:a342fc078a9dc1a340c380c1f58626d187bd881d50863b55317da685a39ecb75","target":"record","created_at":"2026-05-18T02:15:14Z","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":"69287ae23b3aef241aa7f6d5ad3f876ce1981b201d0545fca62c2bdfa5a52c1c","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2008-11-19T10:18:19Z","title_canon_sha256":"a8e269f96ab20814cef8ef65ce0c903b26d994b91a9447d23f046d35e58539c8"},"schema_version":"1.0","source":{"id":"0811.3073","kind":"arxiv","version":2}},"canonical_sha256":"5129a9a7e52a07b1e6701a2d733c1f449bb958bb37a0e095816da0e19e13c48d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5129a9a7e52a07b1e6701a2d733c1f449bb958bb37a0e095816da0e19e13c48d","first_computed_at":"2026-05-18T02:15:14.004106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:14.004106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yxB8oyU8sQXHsweBZDsRnSTUjadf2EIG4qGo26OxQjtEnGnpUdFaDk2CvZr8PInd8n+OA/v1hqiaIYLxjunmAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:14.004793Z","signed_message":"canonical_sha256_bytes"},"source_id":"0811.3073","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a342fc078a9dc1a340c380c1f58626d187bd881d50863b55317da685a39ecb75","sha256:b3f5e89fde02fd39a05aecb9c4d9227a2b1445f0c830a9c2737efd89905222f0"],"state_sha256":"955fc346e74f24fc78f6ba9149e620d3f36039a87bae07d61d168f9b685ec882"}