{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:HDI5IK5AL3FPMBHVI2N4HHTTEX","short_pith_number":"pith:HDI5IK5A","schema_version":"1.0","canonical_sha256":"38d1d42ba05ecaf604f5469bc39e7325c221cb6f15549edd083ffc684288cb5a","source":{"kind":"arxiv","id":"2606.15173","version":2},"attestation_state":"computed","paper":{"title":"The Holographic Multi-Entropy Cone","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Xin-Xiang Ju, Yang Zhao","submitted_at":"2026-06-13T07:42:33Z","abstract_excerpt":"We generalize the holographic entropy cone (HEC) to the holographic multi-entropy cone (HMEC) by adjoining multi-entropy coordinates to the standard bipartition entropy coordinates. We show that holographic states, through their multi-entropy vectors, form a rational polyhedral cone in multi-entropy space, and multicontraction maps provide exact certificates for holographic multi-entropy inequalities (HMEIs). We determine all facets of the $n=3,4$ HMECs, where $n$ includes the purifier, and obtain seven fundamental HMEI orbits: two for $n=3$ and five for $n=4$. We further propose two structura"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.15173","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-06-13T07:42:33Z","cross_cats_sorted":[],"title_canon_sha256":"24201b5da398b9163e2190d79f4c14b01d4bf499052e0d559ebe6a5c172f91bb","abstract_canon_sha256":"0b3077654943a2ebd21dae6910ce35c5fa70f9b5c4d9239b4db43ef6517bf7c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-15T01:22:00.038894Z","signature_b64":"RUmfJOitKl99TgBmJU3jic1bYDtp6FqPhqNdnJvBMpnit6Nj2EqePU2pevJg8iIPBM9e/Glli4aNREj4H/b0Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38d1d42ba05ecaf604f5469bc39e7325c221cb6f15549edd083ffc684288cb5a","last_reissued_at":"2026-07-15T01:22:00.038027Z","signature_status":"signed_v1","first_computed_at":"2026-07-15T01:22:00.038027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Holographic Multi-Entropy Cone","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Xin-Xiang Ju, Yang Zhao","submitted_at":"2026-06-13T07:42:33Z","abstract_excerpt":"We generalize the holographic entropy cone (HEC) to the holographic multi-entropy cone (HMEC) by adjoining multi-entropy coordinates to the standard bipartition entropy coordinates. We show that holographic states, through their multi-entropy vectors, form a rational polyhedral cone in multi-entropy space, and multicontraction maps provide exact certificates for holographic multi-entropy inequalities (HMEIs). We determine all facets of the $n=3,4$ HMECs, where $n$ includes the purifier, and obtain seven fundamental HMEI orbits: two for $n=3$ and five for $n=4$. We further propose two structura"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.15173","kind":"arxiv","version":2},"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/2606.15173/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.15173","created_at":"2026-07-15T01:22:00.038454+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.15173v2","created_at":"2026-07-15T01:22:00.038454+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.15173","created_at":"2026-07-15T01:22:00.038454+00:00"},{"alias_kind":"pith_short_12","alias_value":"HDI5IK5AL3FP","created_at":"2026-07-15T01:22:00.038454+00:00"},{"alias_kind":"pith_short_16","alias_value":"HDI5IK5AL3FPMBHV","created_at":"2026-07-15T01:22:00.038454+00:00"},{"alias_kind":"pith_short_8","alias_value":"HDI5IK5A","created_at":"2026-07-15T01:22:00.038454+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2606.20790","citing_title":"Complexity Inequalities for Quantum Subsystems","ref_index":18,"is_internal_anchor":true},{"citing_arxiv_id":"2606.00210","citing_title":"Constraints on four-party entanglement in holography","ref_index":41,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HDI5IK5AL3FPMBHVI2N4HHTTEX","json":"https://pith.science/pith/HDI5IK5AL3FPMBHVI2N4HHTTEX.json","graph_json":"https://pith.science/api/pith-number/HDI5IK5AL3FPMBHVI2N4HHTTEX/graph.json","events_json":"https://pith.science/api/pith-number/HDI5IK5AL3FPMBHVI2N4HHTTEX/events.json","paper":"https://pith.science/paper/HDI5IK5A"},"agent_actions":{"view_html":"https://pith.science/pith/HDI5IK5AL3FPMBHVI2N4HHTTEX","download_json":"https://pith.science/pith/HDI5IK5AL3FPMBHVI2N4HHTTEX.json","view_paper":"https://pith.science/paper/HDI5IK5A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.15173&json=true","fetch_graph":"https://pith.science/api/pith-number/HDI5IK5AL3FPMBHVI2N4HHTTEX/graph.json","fetch_events":"https://pith.science/api/pith-number/HDI5IK5AL3FPMBHVI2N4HHTTEX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HDI5IK5AL3FPMBHVI2N4HHTTEX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HDI5IK5AL3FPMBHVI2N4HHTTEX/action/storage_attestation","attest_author":"https://pith.science/pith/HDI5IK5AL3FPMBHVI2N4HHTTEX/action/author_attestation","sign_citation":"https://pith.science/pith/HDI5IK5AL3FPMBHVI2N4HHTTEX/action/citation_signature","submit_replication":"https://pith.science/pith/HDI5IK5AL3FPMBHVI2N4HHTTEX/action/replication_record"}},"created_at":"2026-07-15T01:22:00.038454+00:00","updated_at":"2026-07-15T01:22:00.038454+00:00"}