{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZNIRJ3RLAP24OTMIU72NIMN65W","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":"0e834294ea8a5aeda806a5a8296763362b58d6605c73f2f7028c4e36917cf72a","cross_cats_sorted":["cond-mat.mtrl-sci","cond-mat.soft"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2026-06-16T14:56:26Z","title_canon_sha256":"26a0b9af65fe485fb6eeed09f34159f46507fbabbc23c878a36ade517daac3af"},"schema_version":"1.0","source":{"id":"2606.18014","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.18014","created_at":"2026-06-19T16:10:45Z"},{"alias_kind":"arxiv_version","alias_value":"2606.18014v1","created_at":"2026-06-19T16:10:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.18014","created_at":"2026-06-19T16:10:45Z"},{"alias_kind":"pith_short_12","alias_value":"ZNIRJ3RLAP24","created_at":"2026-06-19T16:10:45Z"},{"alias_kind":"pith_short_16","alias_value":"ZNIRJ3RLAP24OTMI","created_at":"2026-06-19T16:10:45Z"},{"alias_kind":"pith_short_8","alias_value":"ZNIRJ3RL","created_at":"2026-06-19T16:10:45Z"}],"graph_snapshots":[{"event_id":"sha256:577a1b4b3186bc6fd2df3222a9b43ebf325fd74bfab2e9a8de7b17e3d5512425","target":"graph","created_at":"2026-06-19T16:10:45Z","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/2606.18014/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive an effective orbital-lattice model with quantum $S=1$ degrees of freedom for transition-metal compounds, providing a microscopic understanding of cluster formation driven by the cooperative interplay of spin, orbital, and lattice degrees of freedom. Motivated by the trimerized phases observed in LiVS$_2$ and LiVO$_2$, we consider a triangular-lattice three-orbital system with two electrons per site occupying the threefold-degenerate $t_{2g}$ manifold. Starting from a multiorbital Kanamori-Hubbard Hamiltonian, we project the low-energy sector onto the local $S=1$ triplet manifold, in ","authors_text":"Chisa Hotta, Kota Mitsumoto, Soshun Ozaki","cross_cats":["cond-mat.mtrl-sci","cond-mat.soft"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2026-06-16T14:56:26Z","title":"Theory of clusterization in orbitally degenerate transition-metal compounds driven by lattice instabilities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18014","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":"sha256:28396716b129189965ca5eaf1f961ca6931e8a75d8cab3aea22d34853300cbc6","target":"record","created_at":"2026-06-19T16:10:45Z","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":"0e834294ea8a5aeda806a5a8296763362b58d6605c73f2f7028c4e36917cf72a","cross_cats_sorted":["cond-mat.mtrl-sci","cond-mat.soft"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2026-06-16T14:56:26Z","title_canon_sha256":"26a0b9af65fe485fb6eeed09f34159f46507fbabbc23c878a36ade517daac3af"},"schema_version":"1.0","source":{"id":"2606.18014","kind":"arxiv","version":1}},"canonical_sha256":"cb5114ee2b03f5c74d88a7f4d431beed9b14bac23cd7325cfa082d992eb025a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb5114ee2b03f5c74d88a7f4d431beed9b14bac23cd7325cfa082d992eb025a6","first_computed_at":"2026-06-19T16:10:45.872037Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:45.872037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JJwjP+FlWSPJxjfsNsyzXZDwV6TclxmvIe46/RWsqs6nRgYXVsfSjuYYAtmMV4XyPNhfltH9FvRyWTM6HFOJCw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:45.872392Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.18014","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28396716b129189965ca5eaf1f961ca6931e8a75d8cab3aea22d34853300cbc6","sha256:577a1b4b3186bc6fd2df3222a9b43ebf325fd74bfab2e9a8de7b17e3d5512425"],"state_sha256":"b71f1834fc534534193da1d136c894901e65d772d541d829a328c95f19819772"}