{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:22NWWFAHBU7TWACTI5I272FNCP","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":"a03464ac22c539dc7a70209b24be472591831f5e0b899513c4cd66e3d48f42bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-07-21T18:00:00Z","title_canon_sha256":"b098695c99d55fbdb2fc1b606c651ba78ca190908107b998966d005b95e22b59"},"schema_version":"1.0","source":{"id":"2607.19460","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.19460","created_at":"2026-07-23T00:23:50Z"},{"alias_kind":"arxiv_version","alias_value":"2607.19460v1","created_at":"2026-07-23T00:23:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.19460","created_at":"2026-07-23T00:23:50Z"},{"alias_kind":"pith_short_12","alias_value":"22NWWFAHBU7T","created_at":"2026-07-23T00:23:50Z"},{"alias_kind":"pith_short_16","alias_value":"22NWWFAHBU7TWACT","created_at":"2026-07-23T00:23:50Z"},{"alias_kind":"pith_short_8","alias_value":"22NWWFAH","created_at":"2026-07-23T00:23:50Z"}],"graph_snapshots":[{"event_id":"sha256:2595ffd2baf495a5922eab104e06d60bf243b9dca7bcd65373ef2354fa64b73a","target":"graph","created_at":"2026-07-23T00:23:50Z","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/2607.19460/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Five-dimensional superconformal field theories ($5d$ SCFTs) can be encoded by Generalized Toric Polygons (GTPs), where external legs of the dual $(p,q)$ five-brane web correspond to $T$-cones. Hanany-Witten transitions act on these geometries by flipping $T$-cones about their apex, thereby naturally endowing the choice of origin in the polygon with physical significance. It was recently conjectured that a suitably graded Hilbert series equals the Ehrhart series of the dual polytope, which, in turn, is an invariant under such mutations. In this paper, we introduce a prescription for assigning s","authors_text":"Diego Rodr\\'iguez-G\\'omez, Sebasti\\'an Franco","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-07-21T18:00:00Z","title":"On the Origin of Toric Diagrams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19460","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":"sha256:431dd4d1a60000db6783b16200c905095de1d116f660dad2363de9c972fc0ba7","target":"record","created_at":"2026-07-23T00:23:50Z","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":"a03464ac22c539dc7a70209b24be472591831f5e0b899513c4cd66e3d48f42bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-07-21T18:00:00Z","title_canon_sha256":"b098695c99d55fbdb2fc1b606c651ba78ca190908107b998966d005b95e22b59"},"schema_version":"1.0","source":{"id":"2607.19460","kind":"arxiv","version":1}},"canonical_sha256":"d69b6b14070d3f3b00534751afe8ad13c45d878e0d687f7e2c66a4e578d46ce0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d69b6b14070d3f3b00534751afe8ad13c45d878e0d687f7e2c66a4e578d46ce0","first_computed_at":"2026-07-23T00:23:50.878613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-23T00:23:50.878613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ut9Rjse5KWphBjLYTTW2AV8ctuzAuJg/C33LQdBq8OCiPdfeohmEX40LcRXVLmXB7wfpXsKqxxfgdjwBZmBZAA==","signature_status":"signed_v1","signed_at":"2026-07-23T00:23:50.879426Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.19460","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:431dd4d1a60000db6783b16200c905095de1d116f660dad2363de9c972fc0ba7","sha256:2595ffd2baf495a5922eab104e06d60bf243b9dca7bcd65373ef2354fa64b73a"],"state_sha256":"a2883ad6fc5b63fdcb62f5688fd752dd4e077534c131a365f3f6d98044e8a755"}