{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:JIRS2UXPMF6HWKGKQO3GQ44MJ5","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":"a72654ecce3bec594d061a0ee87ebec72eedfe01e9bf860d43ab96c91698a78b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2026-06-18T09:27:31Z","title_canon_sha256":"b249d5269ec9c02b84c7c31e8771721514bc9be51806f32a316c5964f133330e"},"schema_version":"1.0","source":{"id":"2606.19986","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.19986","created_at":"2026-06-19T16:12:59Z"},{"alias_kind":"arxiv_version","alias_value":"2606.19986v1","created_at":"2026-06-19T16:12:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19986","created_at":"2026-06-19T16:12:59Z"},{"alias_kind":"pith_short_12","alias_value":"JIRS2UXPMF6H","created_at":"2026-06-19T16:12:59Z"},{"alias_kind":"pith_short_16","alias_value":"JIRS2UXPMF6HWKGK","created_at":"2026-06-19T16:12:59Z"},{"alias_kind":"pith_short_8","alias_value":"JIRS2UXP","created_at":"2026-06-19T16:12:59Z"}],"graph_snapshots":[{"event_id":"sha256:da1716e67a6e88e1efc3a7d5f25b244239c86997b7c7c1ad0ed716fbac8a7a50","target":"graph","created_at":"2026-06-19T16:12:59Z","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/2606.19986/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Scissors congruence problems involving translations have prompted the study of translation invariant simple valuations. We review this classical theory from a naive and consistent viewpoint: starting from a description of all simple valuations on polygons, we characterize the effect of translation invariance. A description of all polynomial simple valuations is obtained as a bi-product of the adopted approach and as a direct generalization of the translation invariant theory; it appears to be new.","authors_text":"Askold Khovanskii, Valentina Kiritchenko, Vladlen Timorin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2026-06-18T09:27:31Z","title":"Polynomial valuations on plane polygons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19986","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":"sha256:3abb0bf9b9ef6abdb6d4ea73185779caa00843afd9c23c00da07af1a9e83467e","target":"record","created_at":"2026-06-19T16:12:59Z","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":"a72654ecce3bec594d061a0ee87ebec72eedfe01e9bf860d43ab96c91698a78b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2026-06-18T09:27:31Z","title_canon_sha256":"b249d5269ec9c02b84c7c31e8771721514bc9be51806f32a316c5964f133330e"},"schema_version":"1.0","source":{"id":"2606.19986","kind":"arxiv","version":1}},"canonical_sha256":"4a232d52ef617c7b28ca83b668738c4f485f5c35389d2ecc226fbd8cd1e1be2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a232d52ef617c7b28ca83b668738c4f485f5c35389d2ecc226fbd8cd1e1be2f","first_computed_at":"2026-06-19T16:12:59.868906Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:12:59.868906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F4vqBYKP1WbQtc/EPH2xyvs8KaJQDvAp4Pg7xAPtySrBG8dTqZ95FwGuz0UrUaQRXytkDmXzXXfVjvoSUqwrBA==","signature_status":"signed_v1","signed_at":"2026-06-19T16:12:59.869256Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.19986","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3abb0bf9b9ef6abdb6d4ea73185779caa00843afd9c23c00da07af1a9e83467e","sha256:da1716e67a6e88e1efc3a7d5f25b244239c86997b7c7c1ad0ed716fbac8a7a50"],"state_sha256":"f749586594df866178a05c05ff60478afdfd3406332b46b6db3d22d281e82426"}