{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:SKXI7Q7HVIUXGIEWFSPAQN2AYA","short_pith_number":"pith:SKXI7Q7H","canonical_record":{"source":{"id":"1205.2449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-11T08:07:24Z","cross_cats_sorted":["math.MP","math.NA"],"title_canon_sha256":"0dbeb361e1b525dbea6a317ce6fee8e9e7c12b665e198502339fde8427752a25","abstract_canon_sha256":"5d136d180132f7b065a10a9887566291e28b61ae12d4bb0ad107a606bba639d9"},"schema_version":"1.0"},"canonical_sha256":"92ae8fc3e7aa297320962c9e083740c02837a961e5c815cddd93058af268ea04","source":{"kind":"arxiv","id":"1205.2449","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2449","created_at":"2026-05-18T03:55:55Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2449v1","created_at":"2026-05-18T03:55:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2449","created_at":"2026-05-18T03:55:55Z"},{"alias_kind":"pith_short_12","alias_value":"SKXI7Q7HVIUX","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SKXI7Q7HVIUXGIEW","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SKXI7Q7H","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:SKXI7Q7HVIUXGIEWFSPAQN2AYA","target":"record","payload":{"canonical_record":{"source":{"id":"1205.2449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-11T08:07:24Z","cross_cats_sorted":["math.MP","math.NA"],"title_canon_sha256":"0dbeb361e1b525dbea6a317ce6fee8e9e7c12b665e198502339fde8427752a25","abstract_canon_sha256":"5d136d180132f7b065a10a9887566291e28b61ae12d4bb0ad107a606bba639d9"},"schema_version":"1.0"},"canonical_sha256":"92ae8fc3e7aa297320962c9e083740c02837a961e5c815cddd93058af268ea04","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:55.494663Z","signature_b64":"Sv0GzKbhBEcYeWidOBqLCIg2FxsFop0yDjzBtTWO3RFO+E8kIrL8jCAQng2zJykp4fJWB5BJlPs2WJq9PTn3Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92ae8fc3e7aa297320962c9e083740c02837a961e5c815cddd93058af268ea04","last_reissued_at":"2026-05-18T03:55:55.494135Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:55.494135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.2449","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":"2026-05-18T03:55:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4XWSvNhOwQP9zEWLoG7G0oLSB0ZSHo6c0iI9Ucq+s5eZ2Cj14Qa15euSh2r5ZmqXHEWXgPefpKBFMr2f3W4XBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T04:58:08.305954Z"},"content_sha256":"7d8c901c070c703b8f1e6b2dca3c799c2d747577d40cd5db01ef5c50a3be6d28","schema_version":"1.0","event_id":"sha256:7d8c901c070c703b8f1e6b2dca3c799c2d747577d40cd5db01ef5c50a3be6d28"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:SKXI7Q7HVIUXGIEWFSPAQN2AYA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simulation of a Heat Transfer in Porous Media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.NA"],"primary_cat":"math-ph","authors_text":"Juergen Geiser","submitted_at":"2012-05-11T08:07:24Z","abstract_excerpt":"We are motivated to model a heat transfer to a multiple layer regime and their optimization for heat energy resources. Such a problem can be modeled by a porous media with different phases (liquid and solid).\n  The idea arose of a geothermal energy reservoir which can be used by cities, e.g. Berlin.\n  While hot ground areas are covered to most high populated cites, the energy resources are important and a shift to use such resources are enormous.\n  We design a model of the heat transport via the flow of water through the heterogeneous layer of the underlying earth sediments.\n  We discuss a mul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2449","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:55:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sEAWHAkVPp48PC22Wo6QM90yuA3gs0Ny3BZlCvKUHj9vR0/mw5HIUmJ3yWux3k3on5XhDS2O3qkqgrZ+v0FmBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T04:58:08.306328Z"},"content_sha256":"d7747d55ea419617e1df0464ff10025430ae707b2df16583746a30058a023fa6","schema_version":"1.0","event_id":"sha256:d7747d55ea419617e1df0464ff10025430ae707b2df16583746a30058a023fa6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SKXI7Q7HVIUXGIEWFSPAQN2AYA/bundle.json","state_url":"https://pith.science/pith/SKXI7Q7HVIUXGIEWFSPAQN2AYA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SKXI7Q7HVIUXGIEWFSPAQN2AYA/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":"2026-06-28T04:58:08Z","links":{"resolver":"https://pith.science/pith/SKXI7Q7HVIUXGIEWFSPAQN2AYA","bundle":"https://pith.science/pith/SKXI7Q7HVIUXGIEWFSPAQN2AYA/bundle.json","state":"https://pith.science/pith/SKXI7Q7HVIUXGIEWFSPAQN2AYA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SKXI7Q7HVIUXGIEWFSPAQN2AYA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SKXI7Q7HVIUXGIEWFSPAQN2AYA","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":"5d136d180132f7b065a10a9887566291e28b61ae12d4bb0ad107a606bba639d9","cross_cats_sorted":["math.MP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-11T08:07:24Z","title_canon_sha256":"0dbeb361e1b525dbea6a317ce6fee8e9e7c12b665e198502339fde8427752a25"},"schema_version":"1.0","source":{"id":"1205.2449","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2449","created_at":"2026-05-18T03:55:55Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2449v1","created_at":"2026-05-18T03:55:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2449","created_at":"2026-05-18T03:55:55Z"},{"alias_kind":"pith_short_12","alias_value":"SKXI7Q7HVIUX","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SKXI7Q7HVIUXGIEW","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SKXI7Q7H","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:d7747d55ea419617e1df0464ff10025430ae707b2df16583746a30058a023fa6","target":"graph","created_at":"2026-05-18T03:55:55Z","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":"We are motivated to model a heat transfer to a multiple layer regime and their optimization for heat energy resources. Such a problem can be modeled by a porous media with different phases (liquid and solid).\n  The idea arose of a geothermal energy reservoir which can be used by cities, e.g. Berlin.\n  While hot ground areas are covered to most high populated cites, the energy resources are important and a shift to use such resources are enormous.\n  We design a model of the heat transport via the flow of water through the heterogeneous layer of the underlying earth sediments.\n  We discuss a mul","authors_text":"Juergen Geiser","cross_cats":["math.MP","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-11T08:07:24Z","title":"Simulation of a Heat Transfer in Porous Media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2449","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":"sha256:7d8c901c070c703b8f1e6b2dca3c799c2d747577d40cd5db01ef5c50a3be6d28","target":"record","created_at":"2026-05-18T03:55:55Z","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":"5d136d180132f7b065a10a9887566291e28b61ae12d4bb0ad107a606bba639d9","cross_cats_sorted":["math.MP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-11T08:07:24Z","title_canon_sha256":"0dbeb361e1b525dbea6a317ce6fee8e9e7c12b665e198502339fde8427752a25"},"schema_version":"1.0","source":{"id":"1205.2449","kind":"arxiv","version":1}},"canonical_sha256":"92ae8fc3e7aa297320962c9e083740c02837a961e5c815cddd93058af268ea04","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92ae8fc3e7aa297320962c9e083740c02837a961e5c815cddd93058af268ea04","first_computed_at":"2026-05-18T03:55:55.494135Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:55.494135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Sv0GzKbhBEcYeWidOBqLCIg2FxsFop0yDjzBtTWO3RFO+E8kIrL8jCAQng2zJykp4fJWB5BJlPs2WJq9PTn3Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:55.494663Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.2449","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d8c901c070c703b8f1e6b2dca3c799c2d747577d40cd5db01ef5c50a3be6d28","sha256:d7747d55ea419617e1df0464ff10025430ae707b2df16583746a30058a023fa6"],"state_sha256":"d0fc47b801e8a7563f229f8a9e88be8da7cadbb6c7db7d21d071ae5e73a6298b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UD4rtcv9RyFZx4y0Cy/AKFljPEXlNEXRzetct6Dq+JlGSvOCljgRHBzpMcsiI2Q6bPRbQ464twKkjpw3Bw0jBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T04:58:08.308203Z","bundle_sha256":"300c736763f4aaae7cf6c21d6072b9020ff50e33e22770f128e7f63240e2d6ad"}}