{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:62ONJ7SIWEZFKP32SHBBSREDFR","short_pith_number":"pith:62ONJ7SI","canonical_record":{"source":{"id":"cond-mat/0508343","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-08-14T23:05:29Z","cross_cats_sorted":[],"title_canon_sha256":"a6273c7229159c914762904d8469dda7e19c1b711a36ee4fc79b6d988f668987","abstract_canon_sha256":"6f99444221037f5b11c8ddcb72e7ef12329f7b55a521ddad9af37e5b40970b42"},"schema_version":"1.0"},"canonical_sha256":"f69cd4fe48b132553f7a91c21944832c69d684e97ea4c2c6a51f0c98b560534c","source":{"kind":"arxiv","id":"cond-mat/0508343","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0508343","created_at":"2026-05-18T01:06:52Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0508343v1","created_at":"2026-05-18T01:06:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0508343","created_at":"2026-05-18T01:06:52Z"},{"alias_kind":"pith_short_12","alias_value":"62ONJ7SIWEZF","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"62ONJ7SIWEZFKP32","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"62ONJ7SI","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:62ONJ7SIWEZFKP32SHBBSREDFR","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0508343","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-08-14T23:05:29Z","cross_cats_sorted":[],"title_canon_sha256":"a6273c7229159c914762904d8469dda7e19c1b711a36ee4fc79b6d988f668987","abstract_canon_sha256":"6f99444221037f5b11c8ddcb72e7ef12329f7b55a521ddad9af37e5b40970b42"},"schema_version":"1.0"},"canonical_sha256":"f69cd4fe48b132553f7a91c21944832c69d684e97ea4c2c6a51f0c98b560534c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:52.455007Z","signature_b64":"FHSFdYO1+74pakbMiAqqwNeWU3Kj1c59EjKTIBxmGVZIhJIAhoicYNLMVkUel5lfj9y+F1HHqvpoFzWY0oHDAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f69cd4fe48b132553f7a91c21944832c69d684e97ea4c2c6a51f0c98b560534c","last_reissued_at":"2026-05-18T01:06:52.454407Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:52.454407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0508343","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":"2026-05-18T01:06:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DoyDWouKXiwTNnPAoCPe9cEjiiGq5b0mB+MFjFYAMPOWhQuZZdeUS5FcPnD0toIlwSm9Dv9e7M1i87cTeRwsDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T21:45:31.435875Z"},"content_sha256":"466c4d3698d2cc1e842ace7e666d9cf53bacc33c9f6ddb8422cbb9809f021772","schema_version":"1.0","event_id":"sha256:466c4d3698d2cc1e842ace7e666d9cf53bacc33c9f6ddb8422cbb9809f021772"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:62ONJ7SIWEZFKP32SHBBSREDFR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Logarithmic diffusion and porous media equations: a unified description","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"E. K. Lenzi, I. T. Pedron, L. C. Malacarne, R. S. Mendes, T. J. Buratta","submitted_at":"2005-08-14T23:05:29Z","abstract_excerpt":"In this work we present the logarithmic diffusion equation as a limit case when the index that characterizes a nonlinear Fokker-Planck equation, in its diffusive term, goes to zero. A linear drift and a source term are considered in this equation. Its solution has a lorentzian form, consequently this equation characterizes a super diffusion like a L\\'evy kind. In addition is obtained an equation that unifies the porous media and the logarithmic diffusion equations, including a generalized diffusion equation in fractal dimension. This unification is performed in the nonextensive thermostatistic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0508343","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":"2026-05-18T01:06:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n8+tAgkadAvjzaMsGm6ZuKkELCEvieabn1Qoa+kl60Gv2rL8ct7ZxxBchqnGQ2rffWQQHf2oANZtKQsCMFXfAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T21:45:31.436605Z"},"content_sha256":"b64087712514259068e647a11e4def1f9310092cbaac3884cde8db4d1ae54da6","schema_version":"1.0","event_id":"sha256:b64087712514259068e647a11e4def1f9310092cbaac3884cde8db4d1ae54da6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/62ONJ7SIWEZFKP32SHBBSREDFR/bundle.json","state_url":"https://pith.science/pith/62ONJ7SIWEZFKP32SHBBSREDFR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/62ONJ7SIWEZFKP32SHBBSREDFR/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":"2026-05-29T21:45:31Z","links":{"resolver":"https://pith.science/pith/62ONJ7SIWEZFKP32SHBBSREDFR","bundle":"https://pith.science/pith/62ONJ7SIWEZFKP32SHBBSREDFR/bundle.json","state":"https://pith.science/pith/62ONJ7SIWEZFKP32SHBBSREDFR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/62ONJ7SIWEZFKP32SHBBSREDFR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:62ONJ7SIWEZFKP32SHBBSREDFR","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":"6f99444221037f5b11c8ddcb72e7ef12329f7b55a521ddad9af37e5b40970b42","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-08-14T23:05:29Z","title_canon_sha256":"a6273c7229159c914762904d8469dda7e19c1b711a36ee4fc79b6d988f668987"},"schema_version":"1.0","source":{"id":"cond-mat/0508343","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0508343","created_at":"2026-05-18T01:06:52Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0508343v1","created_at":"2026-05-18T01:06:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0508343","created_at":"2026-05-18T01:06:52Z"},{"alias_kind":"pith_short_12","alias_value":"62ONJ7SIWEZF","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"62ONJ7SIWEZFKP32","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"62ONJ7SI","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:b64087712514259068e647a11e4def1f9310092cbaac3884cde8db4d1ae54da6","target":"graph","created_at":"2026-05-18T01:06:52Z","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 work we present the logarithmic diffusion equation as a limit case when the index that characterizes a nonlinear Fokker-Planck equation, in its diffusive term, goes to zero. A linear drift and a source term are considered in this equation. Its solution has a lorentzian form, consequently this equation characterizes a super diffusion like a L\\'evy kind. In addition is obtained an equation that unifies the porous media and the logarithmic diffusion equations, including a generalized diffusion equation in fractal dimension. This unification is performed in the nonextensive thermostatistic","authors_text":"E. K. Lenzi, I. T. Pedron, L. C. Malacarne, R. S. Mendes, T. J. Buratta","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-08-14T23:05:29Z","title":"Logarithmic diffusion and porous media equations: a unified description"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0508343","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":"sha256:466c4d3698d2cc1e842ace7e666d9cf53bacc33c9f6ddb8422cbb9809f021772","target":"record","created_at":"2026-05-18T01:06:52Z","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":"6f99444221037f5b11c8ddcb72e7ef12329f7b55a521ddad9af37e5b40970b42","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-08-14T23:05:29Z","title_canon_sha256":"a6273c7229159c914762904d8469dda7e19c1b711a36ee4fc79b6d988f668987"},"schema_version":"1.0","source":{"id":"cond-mat/0508343","kind":"arxiv","version":1}},"canonical_sha256":"f69cd4fe48b132553f7a91c21944832c69d684e97ea4c2c6a51f0c98b560534c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f69cd4fe48b132553f7a91c21944832c69d684e97ea4c2c6a51f0c98b560534c","first_computed_at":"2026-05-18T01:06:52.454407Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:52.454407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FHSFdYO1+74pakbMiAqqwNeWU3Kj1c59EjKTIBxmGVZIhJIAhoicYNLMVkUel5lfj9y+F1HHqvpoFzWY0oHDAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:52.455007Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0508343","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:466c4d3698d2cc1e842ace7e666d9cf53bacc33c9f6ddb8422cbb9809f021772","sha256:b64087712514259068e647a11e4def1f9310092cbaac3884cde8db4d1ae54da6"],"state_sha256":"24f5b47dfbb842d11852796f4d1e5fd7d343ff5b883df4bbb6d0a73723586e96"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tI+jyRD7vgyECR7/q4ermHz2Mu6srnk40nuDJ9kJFxsN3nZMcajqjBIHTUK/WMY8C4QmnoTS7F9nDq0AviMKAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T21:45:31.440486Z","bundle_sha256":"ffcfdbe9ba3c66e712262be08f78870a329dbff9cd34d03c2056cb5873a15ae9"}}