{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:MYXWZDRYXTU7KZOIVRREMKC542","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":"42ced0aac4f849e1b9ca28a7bace33a3215d84faa6c48240b3f1c1e9db96a90b","cross_cats_sorted":["cond-mat.stat-mech","math.MP","nlin.PS","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-12-22T08:07:36Z","title_canon_sha256":"4ad4c45b7491d85757c6bae4a8a869a1940bc4abd00f3ad490a2cbb222dbe5fa"},"schema_version":"1.0","source":{"id":"2412.16912","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.16912","created_at":"2026-07-05T09:56:58Z"},{"alias_kind":"arxiv_version","alias_value":"2412.16912v3","created_at":"2026-07-05T09:56:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.16912","created_at":"2026-07-05T09:56:58Z"},{"alias_kind":"pith_short_12","alias_value":"MYXWZDRYXTU7","created_at":"2026-07-05T09:56:58Z"},{"alias_kind":"pith_short_16","alias_value":"MYXWZDRYXTU7KZOI","created_at":"2026-07-05T09:56:58Z"},{"alias_kind":"pith_short_8","alias_value":"MYXWZDRY","created_at":"2026-07-05T09:56:58Z"}],"graph_snapshots":[{"event_id":"sha256:b5acc1c6ede6264f0a6a307f0788fe7ce3edbc610fa49e21f56291bb8ca64abe","target":"graph","created_at":"2026-07-05T09:56:58Z","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/2412.16912/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We carefully review the hierarchical construction by Bouch [Bouch2015] of trees on the square lattice that can be grown from its root in $L!/C^L$ distinct ways, where $L$ denotes the number of bonds constituting the tree, and $C>1$ is a constant. (As discussed in Section IV.A of [ParkerCaoAvdoshkinScaffidiAltman2019] and Appendix A.3 of [ShiraishiTasaki2024], this result has an implication on the operator growth in quantum spin systems in two or higher dimensions.)","authors_text":"Hal Tasaki","cross_cats":["cond-mat.stat-mech","math.MP","nlin.PS","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-12-22T08:07:36Z","title":"Trees that can be grown in \"too many\" ways: A review of Bouch's construction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.16912","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":"sha256:160b1837390343e79b4af3755f36224b43f726909bbb776b4b7639ff9f996429","target":"record","created_at":"2026-07-05T09:56:58Z","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":"42ced0aac4f849e1b9ca28a7bace33a3215d84faa6c48240b3f1c1e9db96a90b","cross_cats_sorted":["cond-mat.stat-mech","math.MP","nlin.PS","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-12-22T08:07:36Z","title_canon_sha256":"4ad4c45b7491d85757c6bae4a8a869a1940bc4abd00f3ad490a2cbb222dbe5fa"},"schema_version":"1.0","source":{"id":"2412.16912","kind":"arxiv","version":3}},"canonical_sha256":"662f6c8e38bce9f565c8ac6246285de68d9376ded2ed309b2f41405a34e9445b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"662f6c8e38bce9f565c8ac6246285de68d9376ded2ed309b2f41405a34e9445b","first_computed_at":"2026-07-05T09:56:58.012946Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:56:58.012946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hIN2jYdX1qClyEAvbs4dhNuWMsQntmV7eT54ExA4SzArDrGPnJ9mOksvetTES21Ut0jdx0OjnbjYFtcd+CUSBg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:56:58.013372Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.16912","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:160b1837390343e79b4af3755f36224b43f726909bbb776b4b7639ff9f996429","sha256:b5acc1c6ede6264f0a6a307f0788fe7ce3edbc610fa49e21f56291bb8ca64abe"],"state_sha256":"e7a83d8f00ec1c23d2e39ef472b7643d404f0467519e4eb3ed2fa6d47eaa5b41"}