{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:EGT6TOKKKNSHO7RLMZKO4NMKJE","short_pith_number":"pith:EGT6TOKK","canonical_record":{"source":{"id":"cond-mat/0007410","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2000-07-26T08:42:48Z","cross_cats_sorted":[],"title_canon_sha256":"4c630c2d82494ceb62b69cc5add4f2e3b7f0f9b091930bde6c107d381c5f9731","abstract_canon_sha256":"159c8db0351284de1272888318fd2593065b0478a3244ffcd1dc11cbe3e2d327"},"schema_version":"1.0"},"canonical_sha256":"21a7e9b94a5364777e2b6654ee358a491b482a185e111cafc745bd67af5b09cb","source":{"kind":"arxiv","id":"cond-mat/0007410","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0007410","created_at":"2026-07-04T16:18:52Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0007410v3","created_at":"2026-07-04T16:18:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0007410","created_at":"2026-07-04T16:18:52Z"},{"alias_kind":"pith_short_12","alias_value":"EGT6TOKKKNSH","created_at":"2026-07-04T16:18:52Z"},{"alias_kind":"pith_short_16","alias_value":"EGT6TOKKKNSHO7RL","created_at":"2026-07-04T16:18:52Z"},{"alias_kind":"pith_short_8","alias_value":"EGT6TOKK","created_at":"2026-07-04T16:18:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:EGT6TOKKKNSHO7RLMZKO4NMKJE","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0007410","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2000-07-26T08:42:48Z","cross_cats_sorted":[],"title_canon_sha256":"4c630c2d82494ceb62b69cc5add4f2e3b7f0f9b091930bde6c107d381c5f9731","abstract_canon_sha256":"159c8db0351284de1272888318fd2593065b0478a3244ffcd1dc11cbe3e2d327"},"schema_version":"1.0"},"canonical_sha256":"21a7e9b94a5364777e2b6654ee358a491b482a185e111cafc745bd67af5b09cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:18:52.287615Z","signature_b64":"+/OYB8+O1Puja/oRnmB/rB5r56rP1dhspltp7TJgqmLA51l6iioyqrBx71f3hDAXIMOtq4+zrC6M1oz0+udPBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21a7e9b94a5364777e2b6654ee358a491b482a185e111cafc745bd67af5b09cb","last_reissued_at":"2026-07-04T16:18:52.287236Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:18:52.287236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0007410","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:18:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tEvWYpbv4cvndtTW2jGtA4Dx6xNQPE0aXXYpYWMgdlLr2rAYmzyLt16MqkZxX1uhaZZZhRK/3NYj8UKCxLQgCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T03:27:09.991562Z"},"content_sha256":"44340df3dd4d8c99375b08ea1e1546675595fbfcc01d74953ecc13b6385209c7","schema_version":"1.0","event_id":"sha256:44340df3dd4d8c99375b08ea1e1546675595fbfcc01d74953ecc13b6385209c7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:EGT6TOKKKNSHO7RLMZKO4NMKJE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transport on Directed Percolation Clusters","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Hans-Karl Janssen, Olaf Stenull","submitted_at":"2000-07-26T08:42:48Z","abstract_excerpt":"We study random lattice networks consisting of resistor like and diode like bonds. For investigating the transport properties of these random resistor diode networks we introduce a field theoretic Hamiltonian amenable to renormalization group analysis. We focus on the average two-port resistance at the transition from the nonpercolating to the directed percolating phase and calculate the corresponding resistance exponent $\\phi$ to two-loop order. Moreover, we determine the backbone dimension $D_B$ of directed percolation clusters to two-loop order. We obtain a scaling relation for $D_B$ that i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0007410","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/cond-mat/0007410/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:18:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6ewmSABLAUZM2FyiQZdjmfHO9xQgcTLGEatwKgT6Vp8mu2Zrd9IeJFBu8thJtVtxm10vbmxadK9kiZShzfODDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T03:27:09.993316Z"},"content_sha256":"d7ab1cd935ef9e856feb1ab4621b3aab95804b756a94001046407e5baf6138c8","schema_version":"1.0","event_id":"sha256:d7ab1cd935ef9e856feb1ab4621b3aab95804b756a94001046407e5baf6138c8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EGT6TOKKKNSHO7RLMZKO4NMKJE/bundle.json","state_url":"https://pith.science/pith/EGT6TOKKKNSHO7RLMZKO4NMKJE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EGT6TOKKKNSHO7RLMZKO4NMKJE/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":"2026-08-20T03:27:09Z","links":{"resolver":"https://pith.science/pith/EGT6TOKKKNSHO7RLMZKO4NMKJE","bundle":"https://pith.science/pith/EGT6TOKKKNSHO7RLMZKO4NMKJE/bundle.json","state":"https://pith.science/pith/EGT6TOKKKNSHO7RLMZKO4NMKJE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EGT6TOKKKNSHO7RLMZKO4NMKJE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:EGT6TOKKKNSHO7RLMZKO4NMKJE","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":"159c8db0351284de1272888318fd2593065b0478a3244ffcd1dc11cbe3e2d327","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2000-07-26T08:42:48Z","title_canon_sha256":"4c630c2d82494ceb62b69cc5add4f2e3b7f0f9b091930bde6c107d381c5f9731"},"schema_version":"1.0","source":{"id":"cond-mat/0007410","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0007410","created_at":"2026-07-04T16:18:52Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0007410v3","created_at":"2026-07-04T16:18:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0007410","created_at":"2026-07-04T16:18:52Z"},{"alias_kind":"pith_short_12","alias_value":"EGT6TOKKKNSH","created_at":"2026-07-04T16:18:52Z"},{"alias_kind":"pith_short_16","alias_value":"EGT6TOKKKNSHO7RL","created_at":"2026-07-04T16:18:52Z"},{"alias_kind":"pith_short_8","alias_value":"EGT6TOKK","created_at":"2026-07-04T16:18:52Z"}],"graph_snapshots":[{"event_id":"sha256:d7ab1cd935ef9e856feb1ab4621b3aab95804b756a94001046407e5baf6138c8","target":"graph","created_at":"2026-07-04T16:18:52Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/cond-mat/0007410/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study random lattice networks consisting of resistor like and diode like bonds. For investigating the transport properties of these random resistor diode networks we introduce a field theoretic Hamiltonian amenable to renormalization group analysis. We focus on the average two-port resistance at the transition from the nonpercolating to the directed percolating phase and calculate the corresponding resistance exponent $\\phi$ to two-loop order. Moreover, we determine the backbone dimension $D_B$ of directed percolation clusters to two-loop order. We obtain a scaling relation for $D_B$ that i","authors_text":"Hans-Karl Janssen, Olaf Stenull","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2000-07-26T08:42:48Z","title":"Transport on Directed Percolation Clusters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0007410","kind":"arxiv","version":3},"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":"sha256:44340df3dd4d8c99375b08ea1e1546675595fbfcc01d74953ecc13b6385209c7","target":"record","created_at":"2026-07-04T16:18:52Z","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":"159c8db0351284de1272888318fd2593065b0478a3244ffcd1dc11cbe3e2d327","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2000-07-26T08:42:48Z","title_canon_sha256":"4c630c2d82494ceb62b69cc5add4f2e3b7f0f9b091930bde6c107d381c5f9731"},"schema_version":"1.0","source":{"id":"cond-mat/0007410","kind":"arxiv","version":3}},"canonical_sha256":"21a7e9b94a5364777e2b6654ee358a491b482a185e111cafc745bd67af5b09cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21a7e9b94a5364777e2b6654ee358a491b482a185e111cafc745bd67af5b09cb","first_computed_at":"2026-07-04T16:18:52.287236Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:18:52.287236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+/OYB8+O1Puja/oRnmB/rB5r56rP1dhspltp7TJgqmLA51l6iioyqrBx71f3hDAXIMOtq4+zrC6M1oz0+udPBg==","signature_status":"signed_v1","signed_at":"2026-07-04T16:18:52.287615Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0007410","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44340df3dd4d8c99375b08ea1e1546675595fbfcc01d74953ecc13b6385209c7","sha256:d7ab1cd935ef9e856feb1ab4621b3aab95804b756a94001046407e5baf6138c8"],"state_sha256":"7752b4e68e48fef085bd4da6d789c2e4474df3a2538f5f3b0ecf0d4eda967c81"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vuxeFg5R5h4sr+q8bK8boXbsgJ7c7j6dc2ZXxCqyQUr0/49RO/T54+oLKJkqL01NGyjmqdkiQTS0ZkhdC2+VCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T03:27:10.001952Z","bundle_sha256":"3aa9207ccbe1da937ebe7fc14515cec14b95b6911a4d0a5f958e942585d91d44"}}