{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3RP3WTQPRJLWOKKJEXMNECQKTB","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":"310580e48831a01f8384368adc47ec3a60ab6a51a5c005e4b4573da42fd36a1e","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-06-09T13:10:35Z","title_canon_sha256":"7df4a8935207ada49bb20dcb5bde0beda992c204598d54daa5c5c48305ce65b9"},"schema_version":"1.0","source":{"id":"1706.02938","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02938","created_at":"2026-05-18T00:05:19Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02938v3","created_at":"2026-05-18T00:05:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02938","created_at":"2026-05-18T00:05:19Z"},{"alias_kind":"pith_short_12","alias_value":"3RP3WTQPRJLW","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3RP3WTQPRJLWOKKJ","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3RP3WTQP","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:047c7324d46287055f49c081e3de3a2ce6d45c9c4e7c29d1b98c618bf5c1528d","target":"graph","created_at":"2026-05-18T00:05:19Z","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":"Spatial modulation has been studied for a long time in condensed matter, nuclear matter and quark matter, so far in non-relativistic field theories. In this paper, spatially modulated vacua at zero temperature and zero density are studied in relativistic field theories. We first propose an adaptation of the Nambu-Goldstone theorem to higher derivative theories under the assumption of the absence of ghosts: when a global symmetry is spontaneously broken due to vacuum expectation values of space-time derivatives of fields, a Nambu-Goldstone (NG) boson appears without a canonical kinetic (quadrat","authors_text":"Muneto Nitta, Ryo Yokokura, Shin Sasaki","cross_cats":["hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-06-09T13:10:35Z","title":"Spatially Modulated Vacua in a Lorentz-invariant Scalar Field Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02938","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":"sha256:3c610904b6deb74bf127d0b347497c404289a95fd4d56dd351d2633120721660","target":"record","created_at":"2026-05-18T00:05:19Z","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":"310580e48831a01f8384368adc47ec3a60ab6a51a5c005e4b4573da42fd36a1e","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-06-09T13:10:35Z","title_canon_sha256":"7df4a8935207ada49bb20dcb5bde0beda992c204598d54daa5c5c48305ce65b9"},"schema_version":"1.0","source":{"id":"1706.02938","kind":"arxiv","version":3}},"canonical_sha256":"dc5fbb4e0f8a5767294925d8d20a0a984f8d711dc8425a5efa39494b7af12392","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc5fbb4e0f8a5767294925d8d20a0a984f8d711dc8425a5efa39494b7af12392","first_computed_at":"2026-05-18T00:05:19.779658Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:19.779658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KbP/9C3S+x6VZB89OQGrH7Ot4FO1hHrIDQWqu9kVo9MwAcCvJJ8pFf9Hw+URGRCY1YnvgcnT5iCkIT2FQSjPBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:19.780119Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.02938","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c610904b6deb74bf127d0b347497c404289a95fd4d56dd351d2633120721660","sha256:047c7324d46287055f49c081e3de3a2ce6d45c9c4e7c29d1b98c618bf5c1528d"],"state_sha256":"0eb35ba31ad9ad50749f6f40f018e59a4277d1c421b631911fe84bbc1c469095"}