{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:OHI3V6RGEJSIR5O7YISXW7CFLR","short_pith_number":"pith:OHI3V6RG","canonical_record":{"source":{"id":"2412.14434","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.str-el","submitted_at":"2024-12-19T01:32:15Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"6fffc66ac7ab57522ce229384c6e24275caee3ce3d7408e0163dba8d7306ac3a","abstract_canon_sha256":"082d448080e3de15e4414747a8058e280809fbabf57005bad07ad2fa7fcc2b3f"},"schema_version":"1.0"},"canonical_sha256":"71d1bafa26226488f5dfc2257b7c455c5a17baa6010cb7a13c89a6be93acf1e0","source":{"kind":"arxiv","id":"2412.14434","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.14434","created_at":"2026-07-05T11:52:46Z"},{"alias_kind":"arxiv_version","alias_value":"2412.14434v3","created_at":"2026-07-05T11:52:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.14434","created_at":"2026-07-05T11:52:46Z"},{"alias_kind":"pith_short_12","alias_value":"OHI3V6RGEJSI","created_at":"2026-07-05T11:52:46Z"},{"alias_kind":"pith_short_16","alias_value":"OHI3V6RGEJSIR5O7","created_at":"2026-07-05T11:52:46Z"},{"alias_kind":"pith_short_8","alias_value":"OHI3V6RG","created_at":"2026-07-05T11:52:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:OHI3V6RGEJSIR5O7YISXW7CFLR","target":"record","payload":{"canonical_record":{"source":{"id":"2412.14434","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.str-el","submitted_at":"2024-12-19T01:32:15Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"6fffc66ac7ab57522ce229384c6e24275caee3ce3d7408e0163dba8d7306ac3a","abstract_canon_sha256":"082d448080e3de15e4414747a8058e280809fbabf57005bad07ad2fa7fcc2b3f"},"schema_version":"1.0"},"canonical_sha256":"71d1bafa26226488f5dfc2257b7c455c5a17baa6010cb7a13c89a6be93acf1e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:52:46.777931Z","signature_b64":"bQWYTbGrFgjDm/0jWlN1/lhcBvuBrZivl7cEZCBNxmK90w1qD69hQzOOYDodrMFDfP5hafl4Vt5TBbQIKIq+CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71d1bafa26226488f5dfc2257b7c455c5a17baa6010cb7a13c89a6be93acf1e0","last_reissued_at":"2026-07-05T11:52:46.777396Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:52:46.777396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.14434","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:52:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9iCiUrgnYxbdE5VeSKt+c6y1VFBbS1vTh48QMx/TAeASYJd/YXwgipdZ8O0iH/A1rc4a8SHGH0ExvqjMTtObCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T21:42:00.380990Z"},"content_sha256":"b2b3046c38ef873a505596d2d89526065d8c7fe4217e765c70524b279f95cc2d","schema_version":"1.0","event_id":"sha256:b2b3046c38ef873a505596d2d89526065d8c7fe4217e765c70524b279f95cc2d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:OHI3V6RGEJSIR5O7YISXW7CFLR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Anomalous Continuous Translations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"cond-mat.str-el","authors_text":"Nathan Seiberg","submitted_at":"2024-12-19T01:32:15Z","abstract_excerpt":"We discuss a large class of non-relativistic continuum field theories where the Euclidean spatial symmetry of the classical theory is violated in the quantum theory by an Adler-Bell-Jackiw-like anomaly. In particular, the continuous translation symmetry of the classical theory is broken in the quantum theory to a discrete symmetry. Furthermore, that discrete symmetry is extended by an internal symmetry, making it non-Abelian. This presentation streamlines and extends the discussion in [1]. In an Appendix, we present an elementary introduction to 't Hooft and Adler-Bell-Jackiw anomalies using a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.14434","kind":"arxiv","version":3},"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/2412.14434/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":"2026-07-05T11:52:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tMwqXOATvDElEgnggFkGSvk4nnkMTEmWFcDhhSowccCDxz6Bn9VPb43TBY01FM2QEHSIep8HcF5XRS3j0HZ9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T21:42:00.381379Z"},"content_sha256":"111478e7d74eb7563f074068dcd17a696b8d8c6bc45ba995ce77be8a78d1049c","schema_version":"1.0","event_id":"sha256:111478e7d74eb7563f074068dcd17a696b8d8c6bc45ba995ce77be8a78d1049c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OHI3V6RGEJSIR5O7YISXW7CFLR/bundle.json","state_url":"https://pith.science/pith/OHI3V6RGEJSIR5O7YISXW7CFLR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OHI3V6RGEJSIR5O7YISXW7CFLR/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":"2026-08-11T21:42:00Z","links":{"resolver":"https://pith.science/pith/OHI3V6RGEJSIR5O7YISXW7CFLR","bundle":"https://pith.science/pith/OHI3V6RGEJSIR5O7YISXW7CFLR/bundle.json","state":"https://pith.science/pith/OHI3V6RGEJSIR5O7YISXW7CFLR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OHI3V6RGEJSIR5O7YISXW7CFLR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:OHI3V6RGEJSIR5O7YISXW7CFLR","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":"082d448080e3de15e4414747a8058e280809fbabf57005bad07ad2fa7fcc2b3f","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.str-el","submitted_at":"2024-12-19T01:32:15Z","title_canon_sha256":"6fffc66ac7ab57522ce229384c6e24275caee3ce3d7408e0163dba8d7306ac3a"},"schema_version":"1.0","source":{"id":"2412.14434","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.14434","created_at":"2026-07-05T11:52:46Z"},{"alias_kind":"arxiv_version","alias_value":"2412.14434v3","created_at":"2026-07-05T11:52:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.14434","created_at":"2026-07-05T11:52:46Z"},{"alias_kind":"pith_short_12","alias_value":"OHI3V6RGEJSI","created_at":"2026-07-05T11:52:46Z"},{"alias_kind":"pith_short_16","alias_value":"OHI3V6RGEJSIR5O7","created_at":"2026-07-05T11:52:46Z"},{"alias_kind":"pith_short_8","alias_value":"OHI3V6RG","created_at":"2026-07-05T11:52:46Z"}],"graph_snapshots":[{"event_id":"sha256:111478e7d74eb7563f074068dcd17a696b8d8c6bc45ba995ce77be8a78d1049c","target":"graph","created_at":"2026-07-05T11:52:46Z","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/2412.14434/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We discuss a large class of non-relativistic continuum field theories where the Euclidean spatial symmetry of the classical theory is violated in the quantum theory by an Adler-Bell-Jackiw-like anomaly. In particular, the continuous translation symmetry of the classical theory is broken in the quantum theory to a discrete symmetry. Furthermore, that discrete symmetry is extended by an internal symmetry, making it non-Abelian. This presentation streamlines and extends the discussion in [1]. In an Appendix, we present an elementary introduction to 't Hooft and Adler-Bell-Jackiw anomalies using a","authors_text":"Nathan Seiberg","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.str-el","submitted_at":"2024-12-19T01:32:15Z","title":"Anomalous Continuous Translations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.14434","kind":"arxiv","version":3},"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:b2b3046c38ef873a505596d2d89526065d8c7fe4217e765c70524b279f95cc2d","target":"record","created_at":"2026-07-05T11:52:46Z","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":"082d448080e3de15e4414747a8058e280809fbabf57005bad07ad2fa7fcc2b3f","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.str-el","submitted_at":"2024-12-19T01:32:15Z","title_canon_sha256":"6fffc66ac7ab57522ce229384c6e24275caee3ce3d7408e0163dba8d7306ac3a"},"schema_version":"1.0","source":{"id":"2412.14434","kind":"arxiv","version":3}},"canonical_sha256":"71d1bafa26226488f5dfc2257b7c455c5a17baa6010cb7a13c89a6be93acf1e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71d1bafa26226488f5dfc2257b7c455c5a17baa6010cb7a13c89a6be93acf1e0","first_computed_at":"2026-07-05T11:52:46.777396Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:52:46.777396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bQWYTbGrFgjDm/0jWlN1/lhcBvuBrZivl7cEZCBNxmK90w1qD69hQzOOYDodrMFDfP5hafl4Vt5TBbQIKIq+CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:52:46.777931Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.14434","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2b3046c38ef873a505596d2d89526065d8c7fe4217e765c70524b279f95cc2d","sha256:111478e7d74eb7563f074068dcd17a696b8d8c6bc45ba995ce77be8a78d1049c"],"state_sha256":"f700d57cf408d1d9c2dd1f7d69d9d3a0a5a09c4e4d163c50367cd4dfbb572c74"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sjGmj88ujs3ttdIfOvrx9pIGTqNYy4NHrG/PKg2DmZdJnnD13uI5W3lwwGsi8p8eAgq3vnEBewF4zv1rOuwLAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T21:42:00.384060Z","bundle_sha256":"bc510353d42092fc71b7c5f1c903892975b8d15e566c0fa0a96c0726643fe0e4"}}