{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:NRKXLH5MXKCALIXMEAOW7QTYSJ","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":"7b957bde62cfdbc48e07af95eb672f3c9f319f557496bc6933be60a1a62b278e","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1999-02-10T11:09:35Z","title_canon_sha256":"0b6ed9fb099450da89d761b747d0a37c2ff07b720099dc075c4271a4ec27be8f"},"schema_version":"1.0","source":{"id":"hep-th/9902069","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9902069","created_at":"2026-07-04T16:14:44Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9902069v1","created_at":"2026-07-04T16:14:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9902069","created_at":"2026-07-04T16:14:44Z"},{"alias_kind":"pith_short_12","alias_value":"NRKXLH5MXKCA","created_at":"2026-07-04T16:14:44Z"},{"alias_kind":"pith_short_16","alias_value":"NRKXLH5MXKCALIXM","created_at":"2026-07-04T16:14:44Z"},{"alias_kind":"pith_short_8","alias_value":"NRKXLH5M","created_at":"2026-07-04T16:14:44Z"}],"graph_snapshots":[{"event_id":"sha256:81a2794843be2692170a43f37360d111bad739c93345d8940903f861ca4128c9","target":"graph","created_at":"2026-07-04T16:14:44Z","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/hep-th/9902069/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a mechanism to break the translational invariance of compactified space spontaneously. As a simple model, we study a real $\\phi^4$ model compactified on $M^{D-1}\\otimes S^1$ in detail, where we impose a nontrivial boundary condition on $\\phi$ for the $S^1$-direction. It is shown that the translational invariance for the $S^1$-direction is spontaneously broken when the radius $R$ of $S^1$ becomes larger than a critical radius $R^*$ and also that the model behaves like a $\\phi^4$ model on a single kink background for $R \\to \\infty$. It is pointed out that spontaneous breakdown of tran","authors_text":"K.Takenaga (I.N.F.N, M. Sakamoto(Kobe Univ.), M. Tachibana(Kobe Univ.), Pisa)","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1999-02-10T11:09:35Z","title":"Spontaneously Broken Translational Invariance of Compactified Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9902069","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:c04cbfa4f12c0405f68f02d54008bf775c8df74d8fccdbbce323edb968e73f8a","target":"record","created_at":"2026-07-04T16:14:44Z","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":"7b957bde62cfdbc48e07af95eb672f3c9f319f557496bc6933be60a1a62b278e","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1999-02-10T11:09:35Z","title_canon_sha256":"0b6ed9fb099450da89d761b747d0a37c2ff07b720099dc075c4271a4ec27be8f"},"schema_version":"1.0","source":{"id":"hep-th/9902069","kind":"arxiv","version":1}},"canonical_sha256":"6c55759facba8405a2ec201d6fc278925fcedad97970ecd457ece76accd9bc51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c55759facba8405a2ec201d6fc278925fcedad97970ecd457ece76accd9bc51","first_computed_at":"2026-07-04T16:14:44.969657Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:14:44.969657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HEiskBrnaTE6MafClVlJ5qLYDJN/cvU0XVbnTSWKAybl7E6kOpVVRbHpv/epmaT9qQ8ppBLNCmM9ob0CRrkBCg==","signature_status":"signed_v1","signed_at":"2026-07-04T16:14:44.970115Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9902069","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c04cbfa4f12c0405f68f02d54008bf775c8df74d8fccdbbce323edb968e73f8a","sha256:81a2794843be2692170a43f37360d111bad739c93345d8940903f861ca4128c9"],"state_sha256":"3203bb1fd9fecfc5ccd86a80af8481f69b6cfc9c9b27ef1a9447f73fcd57c9b9"}