{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:R6M37KSFY7WWQQTWDUXBU7AR4L","short_pith_number":"pith:R6M37KSF","canonical_record":{"source":{"id":"2607.24975","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-07-27T18:28:38Z","cross_cats_sorted":[],"title_canon_sha256":"c0b24d5e5833b8f3a1ae0e165104b461953584eb26b270d4749b895e9c15b6dc","abstract_canon_sha256":"158523fac136330ce1121595fba834031b2542ecfee65b7c5d0b54fc913f563e"},"schema_version":"1.0"},"canonical_sha256":"8f99bfaa45c7ed6842761d2e1a7c11e2fca38344ed0d37c312cef3c875f1e219","source":{"kind":"arxiv","id":"2607.24975","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.24975","created_at":"2026-07-29T00:24:55Z"},{"alias_kind":"arxiv_version","alias_value":"2607.24975v1","created_at":"2026-07-29T00:24:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.24975","created_at":"2026-07-29T00:24:55Z"},{"alias_kind":"pith_short_12","alias_value":"R6M37KSFY7WW","created_at":"2026-07-29T00:24:55Z"},{"alias_kind":"pith_short_16","alias_value":"R6M37KSFY7WWQQTW","created_at":"2026-07-29T00:24:55Z"},{"alias_kind":"pith_short_8","alias_value":"R6M37KSF","created_at":"2026-07-29T00:24:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:R6M37KSFY7WWQQTWDUXBU7AR4L","target":"record","payload":{"canonical_record":{"source":{"id":"2607.24975","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-07-27T18:28:38Z","cross_cats_sorted":[],"title_canon_sha256":"c0b24d5e5833b8f3a1ae0e165104b461953584eb26b270d4749b895e9c15b6dc","abstract_canon_sha256":"158523fac136330ce1121595fba834031b2542ecfee65b7c5d0b54fc913f563e"},"schema_version":"1.0"},"canonical_sha256":"8f99bfaa45c7ed6842761d2e1a7c11e2fca38344ed0d37c312cef3c875f1e219","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-29T00:24:55.927694Z","signature_b64":"KsP0TlYNmQ5AhcEdXazGwTTDNNKZVTAu996paH5gAnUIk4PWTHCKMLAonzyO6NfLr99dUAGMtMsbm/bCn1yyAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f99bfaa45c7ed6842761d2e1a7c11e2fca38344ed0d37c312cef3c875f1e219","last_reissued_at":"2026-07-29T00:24:55.926831Z","signature_status":"signed_v1","first_computed_at":"2026-07-29T00:24:55.926831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.24975","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":"2026-07-29T00:24:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VArFPf2xwQFA/19hsoq1NgEfSlG4+PPkT8rITKaSZKkNv1c2DHkjZCBGcoCzgpcfUqnFKT6VGgkqLXfxkYxzAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T11:15:38.573727Z"},"content_sha256":"971a619b946118c31520c9e1e11e26b06a354b05d5d600c85ed8175dd322db8c","schema_version":"1.0","event_id":"sha256:971a619b946118c31520c9e1e11e26b06a354b05d5d600c85ed8175dd322db8c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:R6M37KSFY7WWQQTWDUXBU7AR4L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strongly-connected percolation on directed lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"M. E. J. Newman, P. Grassberger, R. M. Ziff","submitted_at":"2026-07-27T18:28:38Z","abstract_excerpt":"We study percolation on lattices with directed bonds, focusing on the behavior of strongly-connected percolation clusters -- clusters in which every site is reachable from every other along a directed path. We consider the two-dimensional square lattice and various globally isotropic arrangements of the directions of the bonds. Performing simulations using a range of algorithmic approaches, we calculate high-precision values for critical exponents, fractal dimensions, crossing probabilities, and percolation thresholds for bond percolation with each bond arrangement. We find that the critical b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24975","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.24975/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":"2026-07-29T00:24:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SibZ9xbRevyESzXvWOCl5HSwkFNYu++2K+Sp92zEcJJa9GIgSR3uS60wZtCNRGBQaZgRh4EjM/Ilu9OwcpN8Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T11:15:38.574220Z"},"content_sha256":"06c9839e0562fc41d11f6725790821477b8b8c19249e899eda859f487a8ac8b9","schema_version":"1.0","event_id":"sha256:06c9839e0562fc41d11f6725790821477b8b8c19249e899eda859f487a8ac8b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R6M37KSFY7WWQQTWDUXBU7AR4L/bundle.json","state_url":"https://pith.science/pith/R6M37KSFY7WWQQTWDUXBU7AR4L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R6M37KSFY7WWQQTWDUXBU7AR4L/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":"2026-08-12T11:15:38Z","links":{"resolver":"https://pith.science/pith/R6M37KSFY7WWQQTWDUXBU7AR4L","bundle":"https://pith.science/pith/R6M37KSFY7WWQQTWDUXBU7AR4L/bundle.json","state":"https://pith.science/pith/R6M37KSFY7WWQQTWDUXBU7AR4L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R6M37KSFY7WWQQTWDUXBU7AR4L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:R6M37KSFY7WWQQTWDUXBU7AR4L","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":"158523fac136330ce1121595fba834031b2542ecfee65b7c5d0b54fc913f563e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-07-27T18:28:38Z","title_canon_sha256":"c0b24d5e5833b8f3a1ae0e165104b461953584eb26b270d4749b895e9c15b6dc"},"schema_version":"1.0","source":{"id":"2607.24975","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.24975","created_at":"2026-07-29T00:24:55Z"},{"alias_kind":"arxiv_version","alias_value":"2607.24975v1","created_at":"2026-07-29T00:24:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.24975","created_at":"2026-07-29T00:24:55Z"},{"alias_kind":"pith_short_12","alias_value":"R6M37KSFY7WW","created_at":"2026-07-29T00:24:55Z"},{"alias_kind":"pith_short_16","alias_value":"R6M37KSFY7WWQQTW","created_at":"2026-07-29T00:24:55Z"},{"alias_kind":"pith_short_8","alias_value":"R6M37KSF","created_at":"2026-07-29T00:24:55Z"}],"graph_snapshots":[{"event_id":"sha256:06c9839e0562fc41d11f6725790821477b8b8c19249e899eda859f487a8ac8b9","target":"graph","created_at":"2026-07-29T00:24:55Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.24975/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study percolation on lattices with directed bonds, focusing on the behavior of strongly-connected percolation clusters -- clusters in which every site is reachable from every other along a directed path. We consider the two-dimensional square lattice and various globally isotropic arrangements of the directions of the bonds. Performing simulations using a range of algorithmic approaches, we calculate high-precision values for critical exponents, fractal dimensions, crossing probabilities, and percolation thresholds for bond percolation with each bond arrangement. We find that the critical b","authors_text":"M. E. J. Newman, P. Grassberger, R. M. Ziff","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-07-27T18:28:38Z","title":"Strongly-connected percolation on directed lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24975","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":"sha256:971a619b946118c31520c9e1e11e26b06a354b05d5d600c85ed8175dd322db8c","target":"record","created_at":"2026-07-29T00:24:55Z","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":"158523fac136330ce1121595fba834031b2542ecfee65b7c5d0b54fc913f563e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-07-27T18:28:38Z","title_canon_sha256":"c0b24d5e5833b8f3a1ae0e165104b461953584eb26b270d4749b895e9c15b6dc"},"schema_version":"1.0","source":{"id":"2607.24975","kind":"arxiv","version":1}},"canonical_sha256":"8f99bfaa45c7ed6842761d2e1a7c11e2fca38344ed0d37c312cef3c875f1e219","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f99bfaa45c7ed6842761d2e1a7c11e2fca38344ed0d37c312cef3c875f1e219","first_computed_at":"2026-07-29T00:24:55.926831Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-29T00:24:55.926831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KsP0TlYNmQ5AhcEdXazGwTTDNNKZVTAu996paH5gAnUIk4PWTHCKMLAonzyO6NfLr99dUAGMtMsbm/bCn1yyAQ==","signature_status":"signed_v1","signed_at":"2026-07-29T00:24:55.927694Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.24975","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:971a619b946118c31520c9e1e11e26b06a354b05d5d600c85ed8175dd322db8c","sha256:06c9839e0562fc41d11f6725790821477b8b8c19249e899eda859f487a8ac8b9"],"state_sha256":"13166337bd33bcad2f164f543307b15045b907b8dbe2f305b22d96d8ff3e0426"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vJbABAYnrHl9q0UtqqnMkMOziJ40aU/pYSDX5B9aRxwSntndqlE2xKkka98Io6HWsHqAQIfQYU0ehfDua9p5Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T11:15:38.579198Z","bundle_sha256":"bb81c25342b9862bfb07203019fad2e63c15d05cb22d1ded466160d45dbf649b"}}