{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:6RRZ3S6YYDESYLPR3AMU3DFDYA","short_pith_number":"pith:6RRZ3S6Y","schema_version":"1.0","canonical_sha256":"f4639dcbd8c0c92c2df1d8194d8ca3c02b530895d7ccd3eb3211fdea8f14cbfc","source":{"kind":"arxiv","id":"2506.18838","version":3},"attestation_state":"computed","paper":{"title":"Subgraph Entropy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GT","authors_text":"Matt Clay, Tarik Aougab, Tawfiq Hamed","submitted_at":"2025-06-23T16:57:40Z","abstract_excerpt":"Given $r \\geq 3$, we prove that there exists $\\lambda >0$ depending only on $r$ so that if $G$ is a metric graph of rank $r$ with metric entropy $1$, then there exists a proper subgraph $H$ of $G$ with metric entropy at least $\\lambda$. This answers a question of the second two authors together with Rieck. We interpret this as a graph theoretic version of the Bers Lemma from hyperbolic geometry, and explain some connections to the pressure metric on the Culler-Vogtmann Outer Space."},"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":"2506.18838","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2025-06-23T16:57:40Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"14604b593f433446958a5ecf40275c4e6b0c99c3a3686d050badc29fc2258279","abstract_canon_sha256":"ca6e7c5ec7a08f1f47e9a60704ce5dde8c84ed8b692603bf6c16221a414e9a8b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T01:09:37.773640Z","signature_b64":"6iWLKXtwKuJ9O1uyBEVQyxI6UHa+zNTnf0ocgV4iHZJdoRSkD7UfwgOX5MPTRy8+/hFqj51Ya74FCCATgkQIAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4639dcbd8c0c92c2df1d8194d8ca3c02b530895d7ccd3eb3211fdea8f14cbfc","last_reissued_at":"2026-06-04T01:09:37.772990Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T01:09:37.772990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Subgraph Entropy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GT","authors_text":"Matt Clay, Tarik Aougab, Tawfiq Hamed","submitted_at":"2025-06-23T16:57:40Z","abstract_excerpt":"Given $r \\geq 3$, we prove that there exists $\\lambda >0$ depending only on $r$ so that if $G$ is a metric graph of rank $r$ with metric entropy $1$, then there exists a proper subgraph $H$ of $G$ with metric entropy at least $\\lambda$. This answers a question of the second two authors together with Rieck. We interpret this as a graph theoretic version of the Bers Lemma from hyperbolic geometry, and explain some connections to the pressure metric on the Culler-Vogtmann Outer Space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.18838","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.18838/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":"2506.18838","created_at":"2026-06-04T01:09:37.773074+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.18838v3","created_at":"2026-06-04T01:09:37.773074+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.18838","created_at":"2026-06-04T01:09:37.773074+00:00"},{"alias_kind":"pith_short_12","alias_value":"6RRZ3S6YYDES","created_at":"2026-06-04T01:09:37.773074+00:00"},{"alias_kind":"pith_short_16","alias_value":"6RRZ3S6YYDESYLPR","created_at":"2026-06-04T01:09:37.773074+00:00"},{"alias_kind":"pith_short_8","alias_value":"6RRZ3S6Y","created_at":"2026-06-04T01:09:37.773074+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6RRZ3S6YYDESYLPR3AMU3DFDYA","json":"https://pith.science/pith/6RRZ3S6YYDESYLPR3AMU3DFDYA.json","graph_json":"https://pith.science/api/pith-number/6RRZ3S6YYDESYLPR3AMU3DFDYA/graph.json","events_json":"https://pith.science/api/pith-number/6RRZ3S6YYDESYLPR3AMU3DFDYA/events.json","paper":"https://pith.science/paper/6RRZ3S6Y"},"agent_actions":{"view_html":"https://pith.science/pith/6RRZ3S6YYDESYLPR3AMU3DFDYA","download_json":"https://pith.science/pith/6RRZ3S6YYDESYLPR3AMU3DFDYA.json","view_paper":"https://pith.science/paper/6RRZ3S6Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.18838&json=true","fetch_graph":"https://pith.science/api/pith-number/6RRZ3S6YYDESYLPR3AMU3DFDYA/graph.json","fetch_events":"https://pith.science/api/pith-number/6RRZ3S6YYDESYLPR3AMU3DFDYA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6RRZ3S6YYDESYLPR3AMU3DFDYA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6RRZ3S6YYDESYLPR3AMU3DFDYA/action/storage_attestation","attest_author":"https://pith.science/pith/6RRZ3S6YYDESYLPR3AMU3DFDYA/action/author_attestation","sign_citation":"https://pith.science/pith/6RRZ3S6YYDESYLPR3AMU3DFDYA/action/citation_signature","submit_replication":"https://pith.science/pith/6RRZ3S6YYDESYLPR3AMU3DFDYA/action/replication_record"}},"created_at":"2026-06-04T01:09:37.773074+00:00","updated_at":"2026-06-04T01:09:37.773074+00:00"}