{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:6T7M4WSQ5BPZUCZ35TXZU43OKB","short_pith_number":"pith:6T7M4WSQ","canonical_record":{"source":{"id":"2403.17274","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-03-25T23:39:33Z","cross_cats_sorted":[],"title_canon_sha256":"f12b2b3057a817be60a76765ed481f6f69ab84191d215764e7f81e63bdc667d9","abstract_canon_sha256":"ec931b188a5e411a4368fe67f0342311552e6bc527e1149c0ceb615c28b6db50"},"schema_version":"1.0"},"canonical_sha256":"f4fece5a50e85f9a0b3becef9a736e507b2f60b2fe4e931f0c9923bbc18226d2","source":{"kind":"arxiv","id":"2403.17274","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.17274","created_at":"2026-07-05T08:00:47Z"},{"alias_kind":"arxiv_version","alias_value":"2403.17274v1","created_at":"2026-07-05T08:00:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.17274","created_at":"2026-07-05T08:00:47Z"},{"alias_kind":"pith_short_12","alias_value":"6T7M4WSQ5BPZ","created_at":"2026-07-05T08:00:47Z"},{"alias_kind":"pith_short_16","alias_value":"6T7M4WSQ5BPZUCZ3","created_at":"2026-07-05T08:00:47Z"},{"alias_kind":"pith_short_8","alias_value":"6T7M4WSQ","created_at":"2026-07-05T08:00:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:6T7M4WSQ5BPZUCZ35TXZU43OKB","target":"record","payload":{"canonical_record":{"source":{"id":"2403.17274","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-03-25T23:39:33Z","cross_cats_sorted":[],"title_canon_sha256":"f12b2b3057a817be60a76765ed481f6f69ab84191d215764e7f81e63bdc667d9","abstract_canon_sha256":"ec931b188a5e411a4368fe67f0342311552e6bc527e1149c0ceb615c28b6db50"},"schema_version":"1.0"},"canonical_sha256":"f4fece5a50e85f9a0b3becef9a736e507b2f60b2fe4e931f0c9923bbc18226d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:00:47.416461Z","signature_b64":"oG/tIEpF3G6y+nQyj7i5Jb2e3+h68xWadZndC+hwBI/xzMYLeJ1Qu92oOqbEn/ZSJZhwZq+gptJaMQnvnj9JBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4fece5a50e85f9a0b3becef9a736e507b2f60b2fe4e931f0c9923bbc18226d2","last_reissued_at":"2026-07-05T08:00:47.415960Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:00:47.415960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.17274","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:00:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+A6MolCdQV6A7mcgXdP8cyVxhKLGDIcDWGAuUhr1hTI6lhk5IDAwiaWbaShrb1wAlvl6BYxCMywvofNEjXuuDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T16:42:33.116583Z"},"content_sha256":"3adf9c4c6a810330b7d55dfffeb2da96502a9cb1ecd66d6689f22c79002fd7ca","schema_version":"1.0","event_id":"sha256:3adf9c4c6a810330b7d55dfffeb2da96502a9cb1ecd66d6689f22c79002fd7ca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:6T7M4WSQ5BPZUCZ35TXZU43OKB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Worpitzky-compatible sets and the freeness of arrangements between Shi and Catalan","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Takuro Abe, Tan Nhat Tran","submitted_at":"2024-03-25T23:39:33Z","abstract_excerpt":"Given an irreducible root system, the Worpitzky-compatible subsets are defined by a geometric property of the alcoves inside the fundamental parallelepiped of the root system. This concept is motivated and mainly understood through a lattice point counting formula concerning the characteristic and Ehrhart quasi-polynomials. In this paper, we show that the Worpitzky-compatibility has a simple combinatorial characterization in terms of roots. As a byproduct, we obtain a complete characterization by means of Worpitzky-compatibility for the freeness of the arrangements interpolating between the ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.17274","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.17274/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T08:00:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/7cmrXtNk5fY7Mbsoj6E+52XJhpHRwf323urW+710OnCKMillnRuqD6SPlvnNVqilx/gQ451sRxxHLkeDBWCAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T16:42:33.117518Z"},"content_sha256":"a08b2d453bfeb19c5004763c28cc1b3f3e5ddb2274f34be4281041da3f2e9b9f","schema_version":"1.0","event_id":"sha256:a08b2d453bfeb19c5004763c28cc1b3f3e5ddb2274f34be4281041da3f2e9b9f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6T7M4WSQ5BPZUCZ35TXZU43OKB/bundle.json","state_url":"https://pith.science/pith/6T7M4WSQ5BPZUCZ35TXZU43OKB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6T7M4WSQ5BPZUCZ35TXZU43OKB/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":"2026-08-05T16:42:33Z","links":{"resolver":"https://pith.science/pith/6T7M4WSQ5BPZUCZ35TXZU43OKB","bundle":"https://pith.science/pith/6T7M4WSQ5BPZUCZ35TXZU43OKB/bundle.json","state":"https://pith.science/pith/6T7M4WSQ5BPZUCZ35TXZU43OKB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6T7M4WSQ5BPZUCZ35TXZU43OKB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:6T7M4WSQ5BPZUCZ35TXZU43OKB","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":"ec931b188a5e411a4368fe67f0342311552e6bc527e1149c0ceb615c28b6db50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-03-25T23:39:33Z","title_canon_sha256":"f12b2b3057a817be60a76765ed481f6f69ab84191d215764e7f81e63bdc667d9"},"schema_version":"1.0","source":{"id":"2403.17274","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.17274","created_at":"2026-07-05T08:00:47Z"},{"alias_kind":"arxiv_version","alias_value":"2403.17274v1","created_at":"2026-07-05T08:00:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.17274","created_at":"2026-07-05T08:00:47Z"},{"alias_kind":"pith_short_12","alias_value":"6T7M4WSQ5BPZ","created_at":"2026-07-05T08:00:47Z"},{"alias_kind":"pith_short_16","alias_value":"6T7M4WSQ5BPZUCZ3","created_at":"2026-07-05T08:00:47Z"},{"alias_kind":"pith_short_8","alias_value":"6T7M4WSQ","created_at":"2026-07-05T08:00:47Z"}],"graph_snapshots":[{"event_id":"sha256:a08b2d453bfeb19c5004763c28cc1b3f3e5ddb2274f34be4281041da3f2e9b9f","target":"graph","created_at":"2026-07-05T08:00:47Z","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/2403.17274/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given an irreducible root system, the Worpitzky-compatible subsets are defined by a geometric property of the alcoves inside the fundamental parallelepiped of the root system. This concept is motivated and mainly understood through a lattice point counting formula concerning the characteristic and Ehrhart quasi-polynomials. In this paper, we show that the Worpitzky-compatibility has a simple combinatorial characterization in terms of roots. As a byproduct, we obtain a complete characterization by means of Worpitzky-compatibility for the freeness of the arrangements interpolating between the ex","authors_text":"Takuro Abe, Tan Nhat Tran","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-03-25T23:39:33Z","title":"Worpitzky-compatible sets and the freeness of arrangements between Shi and Catalan"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.17274","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":"sha256:3adf9c4c6a810330b7d55dfffeb2da96502a9cb1ecd66d6689f22c79002fd7ca","target":"record","created_at":"2026-07-05T08:00:47Z","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":"ec931b188a5e411a4368fe67f0342311552e6bc527e1149c0ceb615c28b6db50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-03-25T23:39:33Z","title_canon_sha256":"f12b2b3057a817be60a76765ed481f6f69ab84191d215764e7f81e63bdc667d9"},"schema_version":"1.0","source":{"id":"2403.17274","kind":"arxiv","version":1}},"canonical_sha256":"f4fece5a50e85f9a0b3becef9a736e507b2f60b2fe4e931f0c9923bbc18226d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4fece5a50e85f9a0b3becef9a736e507b2f60b2fe4e931f0c9923bbc18226d2","first_computed_at":"2026-07-05T08:00:47.415960Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:00:47.415960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oG/tIEpF3G6y+nQyj7i5Jb2e3+h68xWadZndC+hwBI/xzMYLeJ1Qu92oOqbEn/ZSJZhwZq+gptJaMQnvnj9JBg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:00:47.416461Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.17274","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3adf9c4c6a810330b7d55dfffeb2da96502a9cb1ecd66d6689f22c79002fd7ca","sha256:a08b2d453bfeb19c5004763c28cc1b3f3e5ddb2274f34be4281041da3f2e9b9f"],"state_sha256":"f12aa997a5606587dae9a691063aa96d57a2c7bb4e098c2c420091ae3de44f67"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o/jWTwMClWYZdK9TzOVP0GOYKvAL+fOlIZhBS2V//ERJksCFtbRCNeW2o1lNYp8TY0+hiuf/eh4zdaN9s5U/BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T16:42:33.129495Z","bundle_sha256":"a4279c111cf4fde97e83d4919158849b40ace3edd2b609cd67d05521b0a83354"}}