{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:3VTMRYADWMOPCFB6GJBMALVI53","short_pith_number":"pith:3VTMRYAD","canonical_record":{"source":{"id":"1608.01614","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-04T17:14:11Z","cross_cats_sorted":["math.AC","math.NT"],"title_canon_sha256":"d57ae68470f5207241799e7c24b35963181c1bb4fea53251d537592f4e9cbf15","abstract_canon_sha256":"116b0a033e408c67da1ffd1876eb78cbb279b9ba0c3a716cf67d3131f27877b7"},"schema_version":"1.0"},"canonical_sha256":"dd66c8e003b31cf1143e3242c02ea8eefe82a683c3d6889ed2ee52a5944eb492","source":{"kind":"arxiv","id":"1608.01614","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01614","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01614v3","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01614","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"pith_short_12","alias_value":"3VTMRYADWMOP","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"3VTMRYADWMOPCFB6","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"3VTMRYAD","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:3VTMRYADWMOPCFB6GJBMALVI53","target":"record","payload":{"canonical_record":{"source":{"id":"1608.01614","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-04T17:14:11Z","cross_cats_sorted":["math.AC","math.NT"],"title_canon_sha256":"d57ae68470f5207241799e7c24b35963181c1bb4fea53251d537592f4e9cbf15","abstract_canon_sha256":"116b0a033e408c67da1ffd1876eb78cbb279b9ba0c3a716cf67d3131f27877b7"},"schema_version":"1.0"},"canonical_sha256":"dd66c8e003b31cf1143e3242c02ea8eefe82a683c3d6889ed2ee52a5944eb492","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:29.214755Z","signature_b64":"obnSMlIb7hAAqWhYsceqdZY2WlV9y52HvmpN/IKBRI4fJ9cTRdxXh0i5NtByBKf8fHmw386TsuBBPjlxV6eyBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd66c8e003b31cf1143e3242c02ea8eefe82a683c3d6889ed2ee52a5944eb492","last_reissued_at":"2026-05-18T00:14:29.214189Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:29.214189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.01614","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EhSeYzwx7mawrNmdk+9qY4DgEZtuzpdsdIAmJbYhB0Ow6spVO1R9jwZoV5qS4etfyqWbxUDPkye+krz9N6CaCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:17:23.660498Z"},"content_sha256":"ccd547d499a7d081d51e3219a3e5b13f803454c266ce30db3ff6a918f9e98ce9","schema_version":"1.0","event_id":"sha256:ccd547d499a7d081d51e3219a3e5b13f803454c266ce30db3ff6a918f9e98ce9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:3VTMRYADWMOPCFB6GJBMALVI53","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Detecting the Integer Decomposition Property and Ehrhart Unimodality in Reflexive Simplices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.NT"],"primary_cat":"math.CO","authors_text":"Benjamin Braun, Liam Solus, Robert Davis","submitted_at":"2016-08-04T17:14:11Z","abstract_excerpt":"A long-standing open conjecture in combinatorics asserts that a Gorenstein lattice polytope with the integer decomposition property (IDP) has a unimodal (Ehrhart) $h^\\ast$-polynomial. This conjecture can be viewed as a strengthening of a previously disproved conjecture which stated that any Gorenstein lattice polytope has a unimodal $h^\\ast$-polynomial. The first counterexamples to unimodality for Gorenstein lattice polytopes were given in even dimensions greater than five by Musta{\\c{t}}{\\v{a}} and Payne, and this was extended to all dimensions greater than five by Payne. While there exist nu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01614","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hgMLOKT/l7eCKsNGVxbwPWphLWubxW9tun86q17tzDfJhaVw1RRU40x1xY5fq7O0iqwOkZNGIUSeni9+Ax7MDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:17:23.661100Z"},"content_sha256":"ff98842a9e2ad73bc8308b14a8feb6aa834a3961efd4f3f1ad728d7e3583d93a","schema_version":"1.0","event_id":"sha256:ff98842a9e2ad73bc8308b14a8feb6aa834a3961efd4f3f1ad728d7e3583d93a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3VTMRYADWMOPCFB6GJBMALVI53/bundle.json","state_url":"https://pith.science/pith/3VTMRYADWMOPCFB6GJBMALVI53/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3VTMRYADWMOPCFB6GJBMALVI53/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T00:17:23Z","links":{"resolver":"https://pith.science/pith/3VTMRYADWMOPCFB6GJBMALVI53","bundle":"https://pith.science/pith/3VTMRYADWMOPCFB6GJBMALVI53/bundle.json","state":"https://pith.science/pith/3VTMRYADWMOPCFB6GJBMALVI53/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3VTMRYADWMOPCFB6GJBMALVI53/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3VTMRYADWMOPCFB6GJBMALVI53","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":"116b0a033e408c67da1ffd1876eb78cbb279b9ba0c3a716cf67d3131f27877b7","cross_cats_sorted":["math.AC","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-04T17:14:11Z","title_canon_sha256":"d57ae68470f5207241799e7c24b35963181c1bb4fea53251d537592f4e9cbf15"},"schema_version":"1.0","source":{"id":"1608.01614","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01614","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01614v3","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01614","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"pith_short_12","alias_value":"3VTMRYADWMOP","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"3VTMRYADWMOPCFB6","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"3VTMRYAD","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:ff98842a9e2ad73bc8308b14a8feb6aa834a3961efd4f3f1ad728d7e3583d93a","target":"graph","created_at":"2026-05-18T00:14:29Z","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":"A long-standing open conjecture in combinatorics asserts that a Gorenstein lattice polytope with the integer decomposition property (IDP) has a unimodal (Ehrhart) $h^\\ast$-polynomial. This conjecture can be viewed as a strengthening of a previously disproved conjecture which stated that any Gorenstein lattice polytope has a unimodal $h^\\ast$-polynomial. The first counterexamples to unimodality for Gorenstein lattice polytopes were given in even dimensions greater than five by Musta{\\c{t}}{\\v{a}} and Payne, and this was extended to all dimensions greater than five by Payne. While there exist nu","authors_text":"Benjamin Braun, Liam Solus, Robert Davis","cross_cats":["math.AC","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-04T17:14:11Z","title":"Detecting the Integer Decomposition Property and Ehrhart Unimodality in Reflexive Simplices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01614","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:ccd547d499a7d081d51e3219a3e5b13f803454c266ce30db3ff6a918f9e98ce9","target":"record","created_at":"2026-05-18T00:14:29Z","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":"116b0a033e408c67da1ffd1876eb78cbb279b9ba0c3a716cf67d3131f27877b7","cross_cats_sorted":["math.AC","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-04T17:14:11Z","title_canon_sha256":"d57ae68470f5207241799e7c24b35963181c1bb4fea53251d537592f4e9cbf15"},"schema_version":"1.0","source":{"id":"1608.01614","kind":"arxiv","version":3}},"canonical_sha256":"dd66c8e003b31cf1143e3242c02ea8eefe82a683c3d6889ed2ee52a5944eb492","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd66c8e003b31cf1143e3242c02ea8eefe82a683c3d6889ed2ee52a5944eb492","first_computed_at":"2026-05-18T00:14:29.214189Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:29.214189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"obnSMlIb7hAAqWhYsceqdZY2WlV9y52HvmpN/IKBRI4fJ9cTRdxXh0i5NtByBKf8fHmw386TsuBBPjlxV6eyBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:29.214755Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.01614","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ccd547d499a7d081d51e3219a3e5b13f803454c266ce30db3ff6a918f9e98ce9","sha256:ff98842a9e2ad73bc8308b14a8feb6aa834a3961efd4f3f1ad728d7e3583d93a"],"state_sha256":"a64df402348ae89b0a7746d53c3dd3e76be0d8e7cbedaed19d9193f89295fa39"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h7/2y+Gz3eZ57nPMJCcYdhQCI7fas1Vob2vqUCmiYkWafO17rtiRKTW1JwMc85DjEfnW+QuCZMbuJ8nalph8Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T00:17:23.664893Z","bundle_sha256":"9bec42534a551df4a5684336544f509a2ffd65bb004e294e006e5edab2eccc05"}}