{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:F4WJNW5BJ7QXJF4AMTWNJPBPDN","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":"f37fd7f7de162df4e10eb1b89d26de6fa1469ddf8b54f0e34af5d4cda230b2b9","cross_cats_sorted":["cond-mat.mtrl-sci","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-06-14T16:48:48Z","title_canon_sha256":"559d74b521d2bc4f816cc5d10107d01d0f4903aec210d57fce19f60cca2c8404"},"schema_version":"1.0","source":{"id":"1806.06693","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.06693","created_at":"2026-05-17T23:52:24Z"},{"alias_kind":"arxiv_version","alias_value":"1806.06693v3","created_at":"2026-05-17T23:52:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.06693","created_at":"2026-05-17T23:52:24Z"},{"alias_kind":"pith_short_12","alias_value":"F4WJNW5BJ7QX","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"F4WJNW5BJ7QXJF4A","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"F4WJNW5B","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:fdbe3722868576fa1862392fb5109478e1e3c5140f20d9218d8597140b5bcf85","target":"graph","created_at":"2026-05-17T23:52:24Z","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":"The $\\phi^4$ model has been the \"workhorse\" of the classical Ginzburg--Landau phenomenological theory of phase transitions and, furthermore, the foundation for a large amount of the now-classical developments in nonlinear science. However, the $\\phi^4$ model, in its usual variant (symmetric double-well potential), can only possess two equilibria. Many complex physical systems possess more than two equilibria and, furthermore, the number of equilibria can change as a system parameter (e.g., the temperature in condensed matter physics) is varied. Thus, \"higher-order field theories\" come into pla","authors_text":"Avadh Saxena, Avinash Khare, Ivan C. Christov","cross_cats":["cond-mat.mtrl-sci","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-06-14T16:48:48Z","title":"Higher-order field theories: $\\phi^6$, $\\phi^8$ and beyond"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06693","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":"sha256:6b932920eebb00cfb502bb910e104cbdfea04b1d0e0950646a76e7a3bb1e5603","target":"record","created_at":"2026-05-17T23:52:24Z","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":"f37fd7f7de162df4e10eb1b89d26de6fa1469ddf8b54f0e34af5d4cda230b2b9","cross_cats_sorted":["cond-mat.mtrl-sci","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-06-14T16:48:48Z","title_canon_sha256":"559d74b521d2bc4f816cc5d10107d01d0f4903aec210d57fce19f60cca2c8404"},"schema_version":"1.0","source":{"id":"1806.06693","kind":"arxiv","version":3}},"canonical_sha256":"2f2c96dba14fe174978064ecd4bc2f1b547bc715a794e439db7f1e479628a3f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f2c96dba14fe174978064ecd4bc2f1b547bc715a794e439db7f1e479628a3f6","first_computed_at":"2026-05-17T23:52:24.371111Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:24.371111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0/Vh2NYiWgYmXP6rntuEdTcCBMFvncncIgz9awOPrj/8b2SL4lvTkszNb9DZslcBcy13Iy/s+40k0zwSXPkoDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:24.371595Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.06693","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b932920eebb00cfb502bb910e104cbdfea04b1d0e0950646a76e7a3bb1e5603","sha256:fdbe3722868576fa1862392fb5109478e1e3c5140f20d9218d8597140b5bcf85"],"state_sha256":"65295077d8ac13a7a8643b19abe14dbe85aaecdca0b1c4cfe0881b013024b6d8"}