{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RRSWPU6L45YCJC7IIWF7WDP6ZD","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":"cf25d1272d477a96b572cd3c7d6a9034034b9cb9198922ce2995ffa8186a0784","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-12-31T15:07:30Z","title_canon_sha256":"ba8a5bfb9e806cf19b8a0aa373233a5d64640589f9b18e93c8590ec5cb92fae4"},"schema_version":"1.0","source":{"id":"1512.09305","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.09305","created_at":"2026-05-18T00:51:37Z"},{"alias_kind":"arxiv_version","alias_value":"1512.09305v2","created_at":"2026-05-18T00:51:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.09305","created_at":"2026-05-18T00:51:37Z"},{"alias_kind":"pith_short_12","alias_value":"RRSWPU6L45YC","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RRSWPU6L45YCJC7I","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RRSWPU6L","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:aca1348cc1f588b317ebf6718237c6e02d9f89392fcfe942a1e2114d2286577a","target":"graph","created_at":"2026-05-18T00:51:37Z","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":"In this paper the theory is developed for creating a material in which the heat is transmitted along a given line. This gives a possibility to transfer information using heat signals. This seems to be a novel idea. The technical part of the theory is the construction of the potential $q(x)$. This potential describes the heat equation $u_t = \\Delta u - q(x)u$ in the limiting medium which is obtained after the small impedance particles are distributed in a given domain. A numerical method is also established to construct numerically such a potential.","authors_text":"Alexander G. Ramm, C. Van","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-12-31T15:07:30Z","title":"Creating materials in which heat propagates along a line: theory and numerical results"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09305","kind":"arxiv","version":2},"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":"sha256:13926750eb8ff926090b78cad62c5b924ca29705350aae1c988b71020295964d","target":"record","created_at":"2026-05-18T00:51:37Z","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":"cf25d1272d477a96b572cd3c7d6a9034034b9cb9198922ce2995ffa8186a0784","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-12-31T15:07:30Z","title_canon_sha256":"ba8a5bfb9e806cf19b8a0aa373233a5d64640589f9b18e93c8590ec5cb92fae4"},"schema_version":"1.0","source":{"id":"1512.09305","kind":"arxiv","version":2}},"canonical_sha256":"8c6567d3cbe770248be8458bfb0dfec8de2d04e840515b8819779916263b258b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c6567d3cbe770248be8458bfb0dfec8de2d04e840515b8819779916263b258b","first_computed_at":"2026-05-18T00:51:37.518277Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:37.518277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4K5MLtupIbWltqXF1CNea5vIlRpgfC4F1DuA7RG+tFFEOCkAEqMsmE1yc7bHqvj+SQ+Fl5LuV5h3yXS5lStNBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:37.518877Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.09305","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13926750eb8ff926090b78cad62c5b924ca29705350aae1c988b71020295964d","sha256:aca1348cc1f588b317ebf6718237c6e02d9f89392fcfe942a1e2114d2286577a"],"state_sha256":"26f258f29c90e06c1643d534c824cf6cac1272640080cdcc84e7ff0206d335a1"}