{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:T2ECMO2BPUB3V42SO7VX7M4PA3","short_pith_number":"pith:T2ECMO2B","canonical_record":{"source":{"id":"1110.3629","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-17T10:53:06Z","cross_cats_sorted":["cond-mat.str-el","hep-th","math.MP"],"title_canon_sha256":"f2339e4e0aa9be54a72d1547e72896e07d9c55d4ef7f2f9293bd0681dee5c46a","abstract_canon_sha256":"2303af3b899b22c1f43219e33df57f77791174c10b29746cd2031b25fc965d87"},"schema_version":"1.0"},"canonical_sha256":"9e88263b417d03baf35277eb7fb38f06cfe4db4325252e880297a17cfaa3cc23","source":{"kind":"arxiv","id":"1110.3629","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3629","created_at":"2026-05-18T02:00:11Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3629v1","created_at":"2026-05-18T02:00:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3629","created_at":"2026-05-18T02:00:11Z"},{"alias_kind":"pith_short_12","alias_value":"T2ECMO2BPUB3","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"T2ECMO2BPUB3V42S","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"T2ECMO2B","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:T2ECMO2BPUB3V42SO7VX7M4PA3","target":"record","payload":{"canonical_record":{"source":{"id":"1110.3629","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-17T10:53:06Z","cross_cats_sorted":["cond-mat.str-el","hep-th","math.MP"],"title_canon_sha256":"f2339e4e0aa9be54a72d1547e72896e07d9c55d4ef7f2f9293bd0681dee5c46a","abstract_canon_sha256":"2303af3b899b22c1f43219e33df57f77791174c10b29746cd2031b25fc965d87"},"schema_version":"1.0"},"canonical_sha256":"9e88263b417d03baf35277eb7fb38f06cfe4db4325252e880297a17cfaa3cc23","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:11.627896Z","signature_b64":"ikG55KXELdMOc8QHUmk/BNB0ZG14AUI2WnLzqZkOVBBI4rh/cExwzDBq5ZdD+xPoj2RsAz04DSg9xNjKB84DCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e88263b417d03baf35277eb7fb38f06cfe4db4325252e880297a17cfaa3cc23","last_reissued_at":"2026-05-18T02:00:11.627137Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:11.627137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.3629","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":"2026-05-18T02:00:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KtCMdqitaZKyWRnyEBviAlG/SzqM0Uma+h/VOEkb59ewca+BFfyCkXFBVBcFp3HNhNRC2DC0INgp2he4IebrCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:06:10.275705Z"},"content_sha256":"a41b87549691bc876603210c0bc7ab2bf727d327099263061541ef11a5715e32","schema_version":"1.0","event_id":"sha256:a41b87549691bc876603210c0bc7ab2bf727d327099263061541ef11a5715e32"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:T2ECMO2BPUB3V42SO7VX7M4PA3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A multiplet analysis of spectra in the presence of broken symmetries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Jan Naudts, Tobias Verhulst","submitted_at":"2011-10-17T10:53:06Z","abstract_excerpt":"We introduce the notion of a generalised symmetry M of a hamiltonian H. It is a symmetry which has been broken in a very specific manner, involving ladder operators R and R*. In Theorem 1 these generalised symmetries are characterised in terms of repeated commutators of H with M. Breaking supersymmetry by adding a term linear in the supercharges is discussed as a motivating example. The complex parameter gamma which appears in the definition of a generalised symmetry is necessarily real when the spectrum of M is discrete. Theorem 2 shows that gamma must also be real when the spectrum of H is f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3629","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":"2026-05-18T02:00:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CA6HMJrjblcWDXHDSWBCQnFO5RF893xT3LX25sZKylj2YtuTkF6dZPR4G+HZ+kGRNVEpHNf2ApGBXfOv20TdAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:06:10.276454Z"},"content_sha256":"77d3139272f65e7907858254f4551487cc4e437014b598ba2a526356163d8404","schema_version":"1.0","event_id":"sha256:77d3139272f65e7907858254f4551487cc4e437014b598ba2a526356163d8404"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T2ECMO2BPUB3V42SO7VX7M4PA3/bundle.json","state_url":"https://pith.science/pith/T2ECMO2BPUB3V42SO7VX7M4PA3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T2ECMO2BPUB3V42SO7VX7M4PA3/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":"2026-06-08T19:06:10Z","links":{"resolver":"https://pith.science/pith/T2ECMO2BPUB3V42SO7VX7M4PA3","bundle":"https://pith.science/pith/T2ECMO2BPUB3V42SO7VX7M4PA3/bundle.json","state":"https://pith.science/pith/T2ECMO2BPUB3V42SO7VX7M4PA3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T2ECMO2BPUB3V42SO7VX7M4PA3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:T2ECMO2BPUB3V42SO7VX7M4PA3","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":"2303af3b899b22c1f43219e33df57f77791174c10b29746cd2031b25fc965d87","cross_cats_sorted":["cond-mat.str-el","hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-17T10:53:06Z","title_canon_sha256":"f2339e4e0aa9be54a72d1547e72896e07d9c55d4ef7f2f9293bd0681dee5c46a"},"schema_version":"1.0","source":{"id":"1110.3629","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3629","created_at":"2026-05-18T02:00:11Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3629v1","created_at":"2026-05-18T02:00:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3629","created_at":"2026-05-18T02:00:11Z"},{"alias_kind":"pith_short_12","alias_value":"T2ECMO2BPUB3","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"T2ECMO2BPUB3V42S","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"T2ECMO2B","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:77d3139272f65e7907858254f4551487cc4e437014b598ba2a526356163d8404","target":"graph","created_at":"2026-05-18T02:00:11Z","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 introduce the notion of a generalised symmetry M of a hamiltonian H. It is a symmetry which has been broken in a very specific manner, involving ladder operators R and R*. In Theorem 1 these generalised symmetries are characterised in terms of repeated commutators of H with M. Breaking supersymmetry by adding a term linear in the supercharges is discussed as a motivating example. The complex parameter gamma which appears in the definition of a generalised symmetry is necessarily real when the spectrum of M is discrete. Theorem 2 shows that gamma must also be real when the spectrum of H is f","authors_text":"Jan Naudts, Tobias Verhulst","cross_cats":["cond-mat.str-el","hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-17T10:53:06Z","title":"A multiplet analysis of spectra in the presence of broken symmetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3629","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:a41b87549691bc876603210c0bc7ab2bf727d327099263061541ef11a5715e32","target":"record","created_at":"2026-05-18T02:00:11Z","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":"2303af3b899b22c1f43219e33df57f77791174c10b29746cd2031b25fc965d87","cross_cats_sorted":["cond-mat.str-el","hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-17T10:53:06Z","title_canon_sha256":"f2339e4e0aa9be54a72d1547e72896e07d9c55d4ef7f2f9293bd0681dee5c46a"},"schema_version":"1.0","source":{"id":"1110.3629","kind":"arxiv","version":1}},"canonical_sha256":"9e88263b417d03baf35277eb7fb38f06cfe4db4325252e880297a17cfaa3cc23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e88263b417d03baf35277eb7fb38f06cfe4db4325252e880297a17cfaa3cc23","first_computed_at":"2026-05-18T02:00:11.627137Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:11.627137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ikG55KXELdMOc8QHUmk/BNB0ZG14AUI2WnLzqZkOVBBI4rh/cExwzDBq5ZdD+xPoj2RsAz04DSg9xNjKB84DCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:11.627896Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.3629","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a41b87549691bc876603210c0bc7ab2bf727d327099263061541ef11a5715e32","sha256:77d3139272f65e7907858254f4551487cc4e437014b598ba2a526356163d8404"],"state_sha256":"2dd5bd8e3247fd08d178dbcce9205555694449e493fa74a9d2e7d74e2688e75d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hVjSX/S/wJZvHnZ4fg/6kxhheIPBsRXHEbr/xaKlTOR9ERaVn95AbCagDzpYKz0ILuDX3PBaDyhv6nxSzU8qCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T19:06:10.279222Z","bundle_sha256":"55b31b0cde62b1493129b34a1d476fdfd3dcca28a792cb84644b189dc270e8bd"}}