{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1996:U52VAC4CNZNEUYD7U5UD4O4MAF","short_pith_number":"pith:U52VAC4C","canonical_record":{"source":{"id":"comp-gas/9609001","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"comp-gas","submitted_at":"1996-09-09T18:46:51Z","cross_cats_sorted":["cond-mat.stat-mech","nlin.CG"],"title_canon_sha256":"7a56cbcc8ff6eaeeb3e67490fdb1279a9b25c0154316518efb138b28767969fb","abstract_canon_sha256":"1ffb88f901d4b9dc7673f487cd066d861397b9d7bed0e0de06443d02933f86bd"},"schema_version":"1.0"},"canonical_sha256":"a775500b826e5a4a607fa7683e3b8c0144147fa1724b2e645dde3cf4e427634f","source":{"kind":"arxiv","id":"comp-gas/9609001","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"comp-gas/9609001","created_at":"2026-05-18T01:07:23Z"},{"alias_kind":"arxiv_version","alias_value":"comp-gas/9609001v2","created_at":"2026-05-18T01:07:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.comp-gas/9609001","created_at":"2026-05-18T01:07:23Z"},{"alias_kind":"pith_short_12","alias_value":"U52VAC4CNZNE","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"U52VAC4CNZNEUYD7","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"U52VAC4C","created_at":"2026-05-18T12:25:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1996:U52VAC4CNZNEUYD7U5UD4O4MAF","target":"record","payload":{"canonical_record":{"source":{"id":"comp-gas/9609001","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"comp-gas","submitted_at":"1996-09-09T18:46:51Z","cross_cats_sorted":["cond-mat.stat-mech","nlin.CG"],"title_canon_sha256":"7a56cbcc8ff6eaeeb3e67490fdb1279a9b25c0154316518efb138b28767969fb","abstract_canon_sha256":"1ffb88f901d4b9dc7673f487cd066d861397b9d7bed0e0de06443d02933f86bd"},"schema_version":"1.0"},"canonical_sha256":"a775500b826e5a4a607fa7683e3b8c0144147fa1724b2e645dde3cf4e427634f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:23.700928Z","signature_b64":"hKXHzkdYsSqqDh0e4l01t4x1Pzwv49fEZXRxnszFs1LItK2LL7Yi2uxkc6XokeXAhMwSFQ6VVW/QQrZFnv1yDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a775500b826e5a4a607fa7683e3b8c0144147fa1724b2e645dde3cf4e427634f","last_reissued_at":"2026-05-18T01:07:23.700477Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:23.700477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"comp-gas/9609001","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:07:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I60g4th3Gx4ZKRQi41le68BCudfG3Q+iFoQKySbIE5SgB8ikPc6CDK8IIjI/YvSGwMORCLZ7TE6Lw3TbOmkWDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:25:47.937863Z"},"content_sha256":"e145339b2288fe6556b1ff702e300ca485197b970bb1ccdca98b6de34664b339","schema_version":"1.0","event_id":"sha256:e145339b2288fe6556b1ff702e300ca485197b970bb1ccdca98b6de34664b339"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1996:U52VAC4CNZNEUYD7U5UD4O4MAF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parallel Algorithm and Dynamic Exponent for Diffusion-limited Aggregation","license":"","headline":"","cross_cats":["cond-mat.stat-mech","nlin.CG"],"primary_cat":"comp-gas","authors_text":"J. Machta (U. Massachusetts), K. Moriarty, R. Greenlaw (U. New Hampshire)","submitted_at":"1996-09-09T18:46:51Z","abstract_excerpt":"A parallel algorithm for ``diffusion-limited aggregation'' (DLA) is described and analyzed from the perspective of computational complexity. The dynamic exponent z of the algorithm is defined with respect to the probabilistic parallel random-access machine (PRAM) model of parallel computation according to $T \\sim L^{z}$, where L is the cluster size, T is the running time, and the algorithm uses a number of processors polynomial in L\\@. It is argued that z=D-D_2/2, where D is the fractal dimension and D_2 is the second generalized dimension. Simulations of DLA are carried out to measure D_2 and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"comp-gas/9609001","kind":"arxiv","version":2},"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":"2026-05-18T01:07:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a4fM0mJb99IOLG3fq8hdT9NAKXgu9GcBqClnyTvRi0Svu0IaaaDdP0Dm7IQoxmFyEKHhX5OfP1V9n/SyrvHtDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:25:47.938206Z"},"content_sha256":"8bc6d62d3281ecf5bd5988a10e58f45376cff0434b1674c421e27c8d0436365f","schema_version":"1.0","event_id":"sha256:8bc6d62d3281ecf5bd5988a10e58f45376cff0434b1674c421e27c8d0436365f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U52VAC4CNZNEUYD7U5UD4O4MAF/bundle.json","state_url":"https://pith.science/pith/U52VAC4CNZNEUYD7U5UD4O4MAF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U52VAC4CNZNEUYD7U5UD4O4MAF/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":"2026-06-07T04:25:47Z","links":{"resolver":"https://pith.science/pith/U52VAC4CNZNEUYD7U5UD4O4MAF","bundle":"https://pith.science/pith/U52VAC4CNZNEUYD7U5UD4O4MAF/bundle.json","state":"https://pith.science/pith/U52VAC4CNZNEUYD7U5UD4O4MAF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U52VAC4CNZNEUYD7U5UD4O4MAF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:U52VAC4CNZNEUYD7U5UD4O4MAF","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":"1ffb88f901d4b9dc7673f487cd066d861397b9d7bed0e0de06443d02933f86bd","cross_cats_sorted":["cond-mat.stat-mech","nlin.CG"],"license":"","primary_cat":"comp-gas","submitted_at":"1996-09-09T18:46:51Z","title_canon_sha256":"7a56cbcc8ff6eaeeb3e67490fdb1279a9b25c0154316518efb138b28767969fb"},"schema_version":"1.0","source":{"id":"comp-gas/9609001","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"comp-gas/9609001","created_at":"2026-05-18T01:07:23Z"},{"alias_kind":"arxiv_version","alias_value":"comp-gas/9609001v2","created_at":"2026-05-18T01:07:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.comp-gas/9609001","created_at":"2026-05-18T01:07:23Z"},{"alias_kind":"pith_short_12","alias_value":"U52VAC4CNZNE","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"U52VAC4CNZNEUYD7","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"U52VAC4C","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:8bc6d62d3281ecf5bd5988a10e58f45376cff0434b1674c421e27c8d0436365f","target":"graph","created_at":"2026-05-18T01:07:23Z","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":"A parallel algorithm for ``diffusion-limited aggregation'' (DLA) is described and analyzed from the perspective of computational complexity. The dynamic exponent z of the algorithm is defined with respect to the probabilistic parallel random-access machine (PRAM) model of parallel computation according to $T \\sim L^{z}$, where L is the cluster size, T is the running time, and the algorithm uses a number of processors polynomial in L\\@. It is argued that z=D-D_2/2, where D is the fractal dimension and D_2 is the second generalized dimension. Simulations of DLA are carried out to measure D_2 and","authors_text":"J. Machta (U. Massachusetts), K. Moriarty, R. Greenlaw (U. New Hampshire)","cross_cats":["cond-mat.stat-mech","nlin.CG"],"headline":"","license":"","primary_cat":"comp-gas","submitted_at":"1996-09-09T18:46:51Z","title":"Parallel Algorithm and Dynamic Exponent for Diffusion-limited Aggregation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"comp-gas/9609001","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:e145339b2288fe6556b1ff702e300ca485197b970bb1ccdca98b6de34664b339","target":"record","created_at":"2026-05-18T01:07:23Z","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":"1ffb88f901d4b9dc7673f487cd066d861397b9d7bed0e0de06443d02933f86bd","cross_cats_sorted":["cond-mat.stat-mech","nlin.CG"],"license":"","primary_cat":"comp-gas","submitted_at":"1996-09-09T18:46:51Z","title_canon_sha256":"7a56cbcc8ff6eaeeb3e67490fdb1279a9b25c0154316518efb138b28767969fb"},"schema_version":"1.0","source":{"id":"comp-gas/9609001","kind":"arxiv","version":2}},"canonical_sha256":"a775500b826e5a4a607fa7683e3b8c0144147fa1724b2e645dde3cf4e427634f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a775500b826e5a4a607fa7683e3b8c0144147fa1724b2e645dde3cf4e427634f","first_computed_at":"2026-05-18T01:07:23.700477Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:23.700477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hKXHzkdYsSqqDh0e4l01t4x1Pzwv49fEZXRxnszFs1LItK2LL7Yi2uxkc6XokeXAhMwSFQ6VVW/QQrZFnv1yDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:23.700928Z","signed_message":"canonical_sha256_bytes"},"source_id":"comp-gas/9609001","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e145339b2288fe6556b1ff702e300ca485197b970bb1ccdca98b6de34664b339","sha256:8bc6d62d3281ecf5bd5988a10e58f45376cff0434b1674c421e27c8d0436365f"],"state_sha256":"d3e0d794ecc66644d61af94b6ee1ff52a923c75c4436457f31417157ca6c2b23"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j7WPU62mUVSRNEL6yEppv7Asf2UIBt/WJzpwV/06Sw6UOO4mhysvDYNgMk23LUoy4vUU8BKerFLKsjuZ88ibBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T04:25:47.940101Z","bundle_sha256":"ab194b7be0ebb7b0cffd5158b805346241f3c47930eaef6e86ee0222826973e0"}}