{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:BBYMOTADW2MJMZIUY6NEAWKGQY","short_pith_number":"pith:BBYMOTAD","canonical_record":{"source":{"id":"2312.10139","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2023-12-15T19:00:00Z","cross_cats_sorted":["cond-mat.stat-mech","cond-mat.str-el","hep-ph","math.RT"],"title_canon_sha256":"3d87b328e249bf6010221b579a71e25677674de1b7d32606885c5ad42f0fb518","abstract_canon_sha256":"8d05f8a0dc91ff577e881094d93baaf8a8f607f9521c558ec373454da02edba5"},"schema_version":"1.0"},"canonical_sha256":"0870c74c03b698966514c79a405946862dc5e573942c2c5bd34e882e9133a689","source":{"kind":"arxiv","id":"2312.10139","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.10139","created_at":"2026-07-05T08:36:44Z"},{"alias_kind":"arxiv_version","alias_value":"2312.10139v2","created_at":"2026-07-05T08:36:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.10139","created_at":"2026-07-05T08:36:44Z"},{"alias_kind":"pith_short_12","alias_value":"BBYMOTADW2MJ","created_at":"2026-07-05T08:36:44Z"},{"alias_kind":"pith_short_16","alias_value":"BBYMOTADW2MJMZIU","created_at":"2026-07-05T08:36:44Z"},{"alias_kind":"pith_short_8","alias_value":"BBYMOTAD","created_at":"2026-07-05T08:36:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:BBYMOTADW2MJMZIUY6NEAWKGQY","target":"record","payload":{"canonical_record":{"source":{"id":"2312.10139","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2023-12-15T19:00:00Z","cross_cats_sorted":["cond-mat.stat-mech","cond-mat.str-el","hep-ph","math.RT"],"title_canon_sha256":"3d87b328e249bf6010221b579a71e25677674de1b7d32606885c5ad42f0fb518","abstract_canon_sha256":"8d05f8a0dc91ff577e881094d93baaf8a8f607f9521c558ec373454da02edba5"},"schema_version":"1.0"},"canonical_sha256":"0870c74c03b698966514c79a405946862dc5e573942c2c5bd34e882e9133a689","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:36:44.989023Z","signature_b64":"KsL+3I7XR9x3f+rWvK7sOkpDILLaA9DrvyTbIlQEMLqV+S9CtfdDmc6sZhiUNatsK9uGb9KGpzauacYCUANMCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0870c74c03b698966514c79a405946862dc5e573942c2c5bd34e882e9133a689","last_reissued_at":"2026-07-05T08:36:44.988527Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:36:44.988527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.10139","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:36:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zWuiM8+tx3rsHjuduU39FAtQO6d7Pco7OI1Er9em6jFpZxCqM4CwGp2UpLKFaJLC3xZqez3wXtrfL0nqe6HECQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T17:30:01.145341Z"},"content_sha256":"0642aae13e75725e0cafde5bb4e3f45d290e7f01e07b8b05d40aa890398b1430","schema_version":"1.0","event_id":"sha256:0642aae13e75725e0cafde5bb4e3f45d290e7f01e07b8b05d40aa890398b1430"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:BBYMOTADW2MJMZIUY6NEAWKGQY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constraints on the spectrum of field theories with non-integer $O(N)$ symmetry from quantum evanescence","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","cond-mat.str-el","hep-ph","math.RT"],"primary_cat":"hep-th","authors_text":"Tom Melia, Weiguang Cao, Xiaochuan Lu","submitted_at":"2023-12-15T19:00:00Z","abstract_excerpt":"We identify constraints in the energy spectra of quantum theories that have a global $O(N)$ symmetry, where $N$ is treated as a continuous parameter. We point out that a class of evanescent states fall out of the spectrum at integer values of $N$ in pairs, via an annihilation mechanism. This forces the energies of the states in such a pair to approach equality as $N$ approaches a certain integer, with both states disappearing at precisely integer $N$ and the point of would-be degeneracy. These constraints occur between different irreducible representations of the analytic continuation of $O(N)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.10139","kind":"arxiv","version":2},"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/2312.10139/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":"2026-07-05T08:36:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BQDXCBDVqa5I63cr6GQW3O15ee6xSEgVGAX0GbGIWqqC1oDV/SkH/Gj2KYMiHFR5qmb7SepKO/+cj+wUqzHYAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T17:30:01.146510Z"},"content_sha256":"a33661ff1c44c03b9997b79cdd535ef246a473fa0de2cd2ccc8ad551190a4edf","schema_version":"1.0","event_id":"sha256:a33661ff1c44c03b9997b79cdd535ef246a473fa0de2cd2ccc8ad551190a4edf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BBYMOTADW2MJMZIUY6NEAWKGQY/bundle.json","state_url":"https://pith.science/pith/BBYMOTADW2MJMZIUY6NEAWKGQY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BBYMOTADW2MJMZIUY6NEAWKGQY/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":"2026-08-03T17:30:01Z","links":{"resolver":"https://pith.science/pith/BBYMOTADW2MJMZIUY6NEAWKGQY","bundle":"https://pith.science/pith/BBYMOTADW2MJMZIUY6NEAWKGQY/bundle.json","state":"https://pith.science/pith/BBYMOTADW2MJMZIUY6NEAWKGQY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BBYMOTADW2MJMZIUY6NEAWKGQY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:BBYMOTADW2MJMZIUY6NEAWKGQY","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":"8d05f8a0dc91ff577e881094d93baaf8a8f607f9521c558ec373454da02edba5","cross_cats_sorted":["cond-mat.stat-mech","cond-mat.str-el","hep-ph","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2023-12-15T19:00:00Z","title_canon_sha256":"3d87b328e249bf6010221b579a71e25677674de1b7d32606885c5ad42f0fb518"},"schema_version":"1.0","source":{"id":"2312.10139","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.10139","created_at":"2026-07-05T08:36:44Z"},{"alias_kind":"arxiv_version","alias_value":"2312.10139v2","created_at":"2026-07-05T08:36:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.10139","created_at":"2026-07-05T08:36:44Z"},{"alias_kind":"pith_short_12","alias_value":"BBYMOTADW2MJ","created_at":"2026-07-05T08:36:44Z"},{"alias_kind":"pith_short_16","alias_value":"BBYMOTADW2MJMZIU","created_at":"2026-07-05T08:36:44Z"},{"alias_kind":"pith_short_8","alias_value":"BBYMOTAD","created_at":"2026-07-05T08:36:44Z"}],"graph_snapshots":[{"event_id":"sha256:a33661ff1c44c03b9997b79cdd535ef246a473fa0de2cd2ccc8ad551190a4edf","target":"graph","created_at":"2026-07-05T08:36:44Z","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/2312.10139/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We identify constraints in the energy spectra of quantum theories that have a global $O(N)$ symmetry, where $N$ is treated as a continuous parameter. We point out that a class of evanescent states fall out of the spectrum at integer values of $N$ in pairs, via an annihilation mechanism. This forces the energies of the states in such a pair to approach equality as $N$ approaches a certain integer, with both states disappearing at precisely integer $N$ and the point of would-be degeneracy. These constraints occur between different irreducible representations of the analytic continuation of $O(N)","authors_text":"Tom Melia, Weiguang Cao, Xiaochuan Lu","cross_cats":["cond-mat.stat-mech","cond-mat.str-el","hep-ph","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2023-12-15T19:00:00Z","title":"Constraints on the spectrum of field theories with non-integer $O(N)$ symmetry from quantum evanescence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.10139","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":"sha256:0642aae13e75725e0cafde5bb4e3f45d290e7f01e07b8b05d40aa890398b1430","target":"record","created_at":"2026-07-05T08:36:44Z","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":"8d05f8a0dc91ff577e881094d93baaf8a8f607f9521c558ec373454da02edba5","cross_cats_sorted":["cond-mat.stat-mech","cond-mat.str-el","hep-ph","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2023-12-15T19:00:00Z","title_canon_sha256":"3d87b328e249bf6010221b579a71e25677674de1b7d32606885c5ad42f0fb518"},"schema_version":"1.0","source":{"id":"2312.10139","kind":"arxiv","version":2}},"canonical_sha256":"0870c74c03b698966514c79a405946862dc5e573942c2c5bd34e882e9133a689","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0870c74c03b698966514c79a405946862dc5e573942c2c5bd34e882e9133a689","first_computed_at":"2026-07-05T08:36:44.988527Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:36:44.988527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KsL+3I7XR9x3f+rWvK7sOkpDILLaA9DrvyTbIlQEMLqV+S9CtfdDmc6sZhiUNatsK9uGb9KGpzauacYCUANMCg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:36:44.989023Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.10139","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0642aae13e75725e0cafde5bb4e3f45d290e7f01e07b8b05d40aa890398b1430","sha256:a33661ff1c44c03b9997b79cdd535ef246a473fa0de2cd2ccc8ad551190a4edf"],"state_sha256":"e4c19134648017466afae253daee61f30ac06f0b47e57f0f985dc3d4cefe92b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k2HXpW/GXJvlYWDyAbicEXiv1fl1K9d9AgYlRVN1YtAJlBfFNcnkUPpDmWXKv/bReYe1FrzKq9FEEsaIoyUsBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T17:30:01.153049Z","bundle_sha256":"c90b8ab3cf2ad5ca5aaf9e0adc7c0f56ae97c40fe4ed6800181ff80ee5e45bc5"}}