{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:AUJFK7MZWRSRHFK5FLOHEDXVVO","short_pith_number":"pith:AUJFK7MZ","canonical_record":{"source":{"id":"1502.01859","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-06T11:16:58Z","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.MP"],"title_canon_sha256":"2f92d5a9d3deaa614b87296f045cddef3ee1d18d23131f16abc02ccaa25ee0a9","abstract_canon_sha256":"08563219c6f1dc9585c78eddc931e51e9250f44e627eb564b34b3af057730913"},"schema_version":"1.0"},"canonical_sha256":"0512557d99b46513955d2adc720ef5ab893b9bbf12518c81374de3bd63f10293","source":{"kind":"arxiv","id":"1502.01859","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01859","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01859v1","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01859","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"pith_short_12","alias_value":"AUJFK7MZWRSR","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AUJFK7MZWRSRHFK5","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AUJFK7MZ","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:AUJFK7MZWRSRHFK5FLOHEDXVVO","target":"record","payload":{"canonical_record":{"source":{"id":"1502.01859","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-06T11:16:58Z","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.MP"],"title_canon_sha256":"2f92d5a9d3deaa614b87296f045cddef3ee1d18d23131f16abc02ccaa25ee0a9","abstract_canon_sha256":"08563219c6f1dc9585c78eddc931e51e9250f44e627eb564b34b3af057730913"},"schema_version":"1.0"},"canonical_sha256":"0512557d99b46513955d2adc720ef5ab893b9bbf12518c81374de3bd63f10293","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:08.703845Z","signature_b64":"Q/6PpM+j15jnVvgd6l0PVuehJfips7LETUKhTaPt7uZWkR3w2xXT3xZEVfordgQUGhaZnnwIZOSrO/j/aPTNAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0512557d99b46513955d2adc720ef5ab893b9bbf12518c81374de3bd63f10293","last_reissued_at":"2026-05-18T01:12:08.703376Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:08.703376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.01859","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":"2026-05-18T01:12:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FxjJyw2wYbG6873lfUhEZKAS0CCTWWz2uWD3K2zKg7r7EASrszlHvCKKeCIz5CyNGqUJpGdTJ4WmMC3dT7TGAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:45:30.466858Z"},"content_sha256":"b7cdde1406709919aa6f9c01762cb7fd4a5f03609bb6e2a233e3cdb07c758ec0","schema_version":"1.0","event_id":"sha256:b7cdde1406709919aa6f9c01762cb7fd4a5f03609bb6e2a233e3cdb07c758ec0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:AUJFK7MZWRSRHFK5FLOHEDXVVO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the reality of spectra of $\\boldsymbol{U_q(sl_2)}$-invariant XXZ Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Alexi Morin-Duchesne, Jorgen Rasmussen, Philippe Ruelle, Yvan Saint-Aubin","submitted_at":"2015-02-06T11:16:58Z","abstract_excerpt":"A new inner product is constructed on each standard module over the Temperley-Lieb algebra $\\mathsf{TL}_n(\\beta)$ for $\\beta\\in \\mathbb R$ and $n \\ge 2$. On these modules, the Hamiltonian $h = -\\sum_i e_i$ is shown to be self-adjoint with respect to this inner product. This implies that its action on these modules is diagonalisable with real eigenvalues. A representation theoretic argument shows that the reality of spectra of the Hamiltonian extends to all other Temperley-Lieb representations. In particular, this result applies to the celebrated $U_q(sl_2)$-invariant XXZ Hamiltonian, for all $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01859","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":"2026-05-18T01:12:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9KQknNo0E0VyvoAdd9JMU5K5GiW+A1EyCkHjMcZmslbhvUWRcPXfbwi2H0ClwgDX3aNpT8xTie02ORXxO1a6DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:45:30.467485Z"},"content_sha256":"f29e33f3fdb7c6f92802a31c9668753351fbc4a3e2ec462804e957de1e160c6d","schema_version":"1.0","event_id":"sha256:f29e33f3fdb7c6f92802a31c9668753351fbc4a3e2ec462804e957de1e160c6d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AUJFK7MZWRSRHFK5FLOHEDXVVO/bundle.json","state_url":"https://pith.science/pith/AUJFK7MZWRSRHFK5FLOHEDXVVO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AUJFK7MZWRSRHFK5FLOHEDXVVO/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":"2026-06-07T10:45:30Z","links":{"resolver":"https://pith.science/pith/AUJFK7MZWRSRHFK5FLOHEDXVVO","bundle":"https://pith.science/pith/AUJFK7MZWRSRHFK5FLOHEDXVVO/bundle.json","state":"https://pith.science/pith/AUJFK7MZWRSRHFK5FLOHEDXVVO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AUJFK7MZWRSRHFK5FLOHEDXVVO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AUJFK7MZWRSRHFK5FLOHEDXVVO","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":"08563219c6f1dc9585c78eddc931e51e9250f44e627eb564b34b3af057730913","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-06T11:16:58Z","title_canon_sha256":"2f92d5a9d3deaa614b87296f045cddef3ee1d18d23131f16abc02ccaa25ee0a9"},"schema_version":"1.0","source":{"id":"1502.01859","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01859","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01859v1","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01859","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"pith_short_12","alias_value":"AUJFK7MZWRSR","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AUJFK7MZWRSRHFK5","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AUJFK7MZ","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:f29e33f3fdb7c6f92802a31c9668753351fbc4a3e2ec462804e957de1e160c6d","target":"graph","created_at":"2026-05-18T01:12:08Z","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":"A new inner product is constructed on each standard module over the Temperley-Lieb algebra $\\mathsf{TL}_n(\\beta)$ for $\\beta\\in \\mathbb R$ and $n \\ge 2$. On these modules, the Hamiltonian $h = -\\sum_i e_i$ is shown to be self-adjoint with respect to this inner product. This implies that its action on these modules is diagonalisable with real eigenvalues. A representation theoretic argument shows that the reality of spectra of the Hamiltonian extends to all other Temperley-Lieb representations. In particular, this result applies to the celebrated $U_q(sl_2)$-invariant XXZ Hamiltonian, for all $","authors_text":"Alexi Morin-Duchesne, Jorgen Rasmussen, Philippe Ruelle, Yvan Saint-Aubin","cross_cats":["cond-mat.stat-mech","hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-06T11:16:58Z","title":"On the reality of spectra of $\\boldsymbol{U_q(sl_2)}$-invariant XXZ Hamiltonians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01859","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:b7cdde1406709919aa6f9c01762cb7fd4a5f03609bb6e2a233e3cdb07c758ec0","target":"record","created_at":"2026-05-18T01:12:08Z","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":"08563219c6f1dc9585c78eddc931e51e9250f44e627eb564b34b3af057730913","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-06T11:16:58Z","title_canon_sha256":"2f92d5a9d3deaa614b87296f045cddef3ee1d18d23131f16abc02ccaa25ee0a9"},"schema_version":"1.0","source":{"id":"1502.01859","kind":"arxiv","version":1}},"canonical_sha256":"0512557d99b46513955d2adc720ef5ab893b9bbf12518c81374de3bd63f10293","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0512557d99b46513955d2adc720ef5ab893b9bbf12518c81374de3bd63f10293","first_computed_at":"2026-05-18T01:12:08.703376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:08.703376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q/6PpM+j15jnVvgd6l0PVuehJfips7LETUKhTaPt7uZWkR3w2xXT3xZEVfordgQUGhaZnnwIZOSrO/j/aPTNAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:08.703845Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.01859","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7cdde1406709919aa6f9c01762cb7fd4a5f03609bb6e2a233e3cdb07c758ec0","sha256:f29e33f3fdb7c6f92802a31c9668753351fbc4a3e2ec462804e957de1e160c6d"],"state_sha256":"9459e4bbc79665def59a1b1b6e4075ed2c5837894acc59874661aafce297e099"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q/S2s3MADknq4k1jUagdacIrZbNveYZEn95+a7F22OWKfAb8GEaO8Soe5wDx5BXykYiUZ7Ce5BMb4pYk8pXUCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T10:45:30.470408Z","bundle_sha256":"3ced362e47b1209353488055281e02235a61630cb99d469de47e1f6060f7bc98"}}