{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:AJRNN57J4RZ77BMDPCJZOPZ5ON","short_pith_number":"pith:AJRNN57J","schema_version":"1.0","canonical_sha256":"0262d6f7e9e473ff85837893973f3d73798fef1b2498dbd2427421d9382e644b","source":{"kind":"arxiv","id":"1808.06717","version":1},"attestation_state":"computed","paper":{"title":"Near log-convexity of measured heat in (discrete) time and consequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cs.CC","authors_text":"Mert Sa\\u{g}lam","submitted_at":"2018-08-20T23:07:10Z","abstract_excerpt":"Let $u,v \\in \\mathbb{R}^\\Omega_+$ be positive unit vectors and $S\\in\\mathbb{R}^{\\Omega\\times\\Omega}_+$ be a symmetric substochastic matrix. For an integer $t\\ge 0$, let $m_t = \\smash{\\left\\langle v,S^tu\\right\\rangle}$, which we view as the heat measured by $v$ after an initial heat configuration $u$ is let to diffuse for $t$ time steps according to $S$. Since $S$ is entropy improving, one may intuit that $m_t$ should not change too rapidly over time. We give the following formalizations of this intuition.\n  We prove that $m_{t+2} \\ge m_t^{1+2/t}\\!,$ an inequality studied earlier by Blakley and"},"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":"1808.06717","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-08-20T23:07:10Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"bd4be124d40928a7c3adae6e6c36d04dad42f62e8312725344904a971cf0a7f4","abstract_canon_sha256":"265ff8bfe82c080dbe7a8242fbdb28234cd1f1dbf4f7b2c75627c87981daa3fd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:39.293327Z","signature_b64":"pj1VZrE2/yh6sN/GyTr2iab3UJChJwWZOf/Vrtcp4fYizqh9gyrAUy4wqprhOB793eiEHv5JNj5OGSYW/kGUDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0262d6f7e9e473ff85837893973f3d73798fef1b2498dbd2427421d9382e644b","last_reissued_at":"2026-05-18T00:07:39.292635Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:39.292635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Near log-convexity of measured heat in (discrete) time and consequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cs.CC","authors_text":"Mert Sa\\u{g}lam","submitted_at":"2018-08-20T23:07:10Z","abstract_excerpt":"Let $u,v \\in \\mathbb{R}^\\Omega_+$ be positive unit vectors and $S\\in\\mathbb{R}^{\\Omega\\times\\Omega}_+$ be a symmetric substochastic matrix. For an integer $t\\ge 0$, let $m_t = \\smash{\\left\\langle v,S^tu\\right\\rangle}$, which we view as the heat measured by $v$ after an initial heat configuration $u$ is let to diffuse for $t$ time steps according to $S$. Since $S$ is entropy improving, one may intuit that $m_t$ should not change too rapidly over time. We give the following formalizations of this intuition.\n  We prove that $m_{t+2} \\ge m_t^{1+2/t}\\!,$ an inequality studied earlier by Blakley and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06717","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":""},"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":"1808.06717","created_at":"2026-05-18T00:07:39.292829+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.06717v1","created_at":"2026-05-18T00:07:39.292829+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.06717","created_at":"2026-05-18T00:07:39.292829+00:00"},{"alias_kind":"pith_short_12","alias_value":"AJRNN57J4RZ7","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_16","alias_value":"AJRNN57J4RZ77BMD","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_8","alias_value":"AJRNN57J","created_at":"2026-05-18T12:32:13.499390+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/AJRNN57J4RZ77BMDPCJZOPZ5ON","json":"https://pith.science/pith/AJRNN57J4RZ77BMDPCJZOPZ5ON.json","graph_json":"https://pith.science/api/pith-number/AJRNN57J4RZ77BMDPCJZOPZ5ON/graph.json","events_json":"https://pith.science/api/pith-number/AJRNN57J4RZ77BMDPCJZOPZ5ON/events.json","paper":"https://pith.science/paper/AJRNN57J"},"agent_actions":{"view_html":"https://pith.science/pith/AJRNN57J4RZ77BMDPCJZOPZ5ON","download_json":"https://pith.science/pith/AJRNN57J4RZ77BMDPCJZOPZ5ON.json","view_paper":"https://pith.science/paper/AJRNN57J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.06717&json=true","fetch_graph":"https://pith.science/api/pith-number/AJRNN57J4RZ77BMDPCJZOPZ5ON/graph.json","fetch_events":"https://pith.science/api/pith-number/AJRNN57J4RZ77BMDPCJZOPZ5ON/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AJRNN57J4RZ77BMDPCJZOPZ5ON/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AJRNN57J4RZ77BMDPCJZOPZ5ON/action/storage_attestation","attest_author":"https://pith.science/pith/AJRNN57J4RZ77BMDPCJZOPZ5ON/action/author_attestation","sign_citation":"https://pith.science/pith/AJRNN57J4RZ77BMDPCJZOPZ5ON/action/citation_signature","submit_replication":"https://pith.science/pith/AJRNN57J4RZ77BMDPCJZOPZ5ON/action/replication_record"}},"created_at":"2026-05-18T00:07:39.292829+00:00","updated_at":"2026-05-18T00:07:39.292829+00:00"}