{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:QOJRHYWXTCD7YDKDMLGME4GIWF","short_pith_number":"pith:QOJRHYWX","canonical_record":{"source":{"id":"1010.0279","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-10-02T00:11:44Z","cross_cats_sorted":["nlin.AO"],"title_canon_sha256":"6201dd38cd0710774c65dda22bfd979382b7ef012fd1e7e4faf2190c2b555fec","abstract_canon_sha256":"7aab31a75686ec223e6c6e8b7aa3e093b776827e056d8272b99533572f0a21da"},"schema_version":"1.0"},"canonical_sha256":"839313e2d79887fc0d4362ccc270c8b1639b845e415abe1099b4808c2ae57f7d","source":{"kind":"arxiv","id":"1010.0279","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0279","created_at":"2026-05-18T04:39:40Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0279v2","created_at":"2026-05-18T04:39:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0279","created_at":"2026-05-18T04:39:40Z"},{"alias_kind":"pith_short_12","alias_value":"QOJRHYWXTCD7","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"QOJRHYWXTCD7YDKD","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"QOJRHYWX","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:QOJRHYWXTCD7YDKDMLGME4GIWF","target":"record","payload":{"canonical_record":{"source":{"id":"1010.0279","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-10-02T00:11:44Z","cross_cats_sorted":["nlin.AO"],"title_canon_sha256":"6201dd38cd0710774c65dda22bfd979382b7ef012fd1e7e4faf2190c2b555fec","abstract_canon_sha256":"7aab31a75686ec223e6c6e8b7aa3e093b776827e056d8272b99533572f0a21da"},"schema_version":"1.0"},"canonical_sha256":"839313e2d79887fc0d4362ccc270c8b1639b845e415abe1099b4808c2ae57f7d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:40.768238Z","signature_b64":"P0WdOYKS+S8zCjrErC/3DMiPKSqhhqkh4AoVX1zzwnS1oiz1jKH89ZH7c0M6VpGRNEp/wahvfqjSSPxXF05pBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"839313e2d79887fc0d4362ccc270c8b1639b845e415abe1099b4808c2ae57f7d","last_reissued_at":"2026-05-18T04:39:40.767702Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:40.767702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.0279","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":"2026-05-18T04:39:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v5H8n+48Vw+lEhJfrZYx+VL5wLp1DHBlCFY2tK4Ropj07WfWrRsqxX0kKcsIBxf0GJkZ0cIpLzk7TuMikUUjCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T06:55:13.550972Z"},"content_sha256":"a3fce4c45e57c9a475a12d6ac39baff263335c12f0b0ce946ae387ad58f2482d","schema_version":"1.0","event_id":"sha256:a3fce4c45e57c9a475a12d6ac39baff263335c12f0b0ce946ae387ad58f2482d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:QOJRHYWXTCD7YDKDMLGME4GIWF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sandpile cascades on interacting tree-like networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.AO"],"primary_cat":"cond-mat.dis-nn","authors_text":"Charles D. Brummitt, Elizabeth A. Leicht, Raissa M. D'Souza","submitted_at":"2010-10-02T00:11:44Z","abstract_excerpt":"The vulnerability of an isolated network to cascades is fundamentally affected by its interactions with other networks. Motivated by failures cascading among electrical grids, we study the Bak-Tang-Wiesenfeld sandpile model on two sparsely-coupled random regular graphs. By approximating avalanches (cascades) as a multi-type branching process and using a generalization of Lagrange's expansion to multiple variables, we calculate the distribution of avalanche sizes within each network. Due to coupling, large avalanches in the individual networks are mitigated--in contrast to the conclusion for a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0279","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":"2026-05-18T04:39:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0l8PYTdYCeVhGN2j9rHu7wL6RjmS1rnppXWxHq6Kt5DIHSKeL7LXA4tnZyo0tRMt5gECgGCZaAPLjmhjThzdAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T06:55:13.551334Z"},"content_sha256":"f6e85d9f525e01d9bcbe3409aaf9f3471dedae345388ad731b38cb64f094d1e1","schema_version":"1.0","event_id":"sha256:f6e85d9f525e01d9bcbe3409aaf9f3471dedae345388ad731b38cb64f094d1e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QOJRHYWXTCD7YDKDMLGME4GIWF/bundle.json","state_url":"https://pith.science/pith/QOJRHYWXTCD7YDKDMLGME4GIWF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QOJRHYWXTCD7YDKDMLGME4GIWF/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":"2026-06-25T06:55:13Z","links":{"resolver":"https://pith.science/pith/QOJRHYWXTCD7YDKDMLGME4GIWF","bundle":"https://pith.science/pith/QOJRHYWXTCD7YDKDMLGME4GIWF/bundle.json","state":"https://pith.science/pith/QOJRHYWXTCD7YDKDMLGME4GIWF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QOJRHYWXTCD7YDKDMLGME4GIWF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:QOJRHYWXTCD7YDKDMLGME4GIWF","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":"7aab31a75686ec223e6c6e8b7aa3e093b776827e056d8272b99533572f0a21da","cross_cats_sorted":["nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-10-02T00:11:44Z","title_canon_sha256":"6201dd38cd0710774c65dda22bfd979382b7ef012fd1e7e4faf2190c2b555fec"},"schema_version":"1.0","source":{"id":"1010.0279","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0279","created_at":"2026-05-18T04:39:40Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0279v2","created_at":"2026-05-18T04:39:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0279","created_at":"2026-05-18T04:39:40Z"},{"alias_kind":"pith_short_12","alias_value":"QOJRHYWXTCD7","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"QOJRHYWXTCD7YDKD","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"QOJRHYWX","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:f6e85d9f525e01d9bcbe3409aaf9f3471dedae345388ad731b38cb64f094d1e1","target":"graph","created_at":"2026-05-18T04:39:40Z","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":"The vulnerability of an isolated network to cascades is fundamentally affected by its interactions with other networks. Motivated by failures cascading among electrical grids, we study the Bak-Tang-Wiesenfeld sandpile model on two sparsely-coupled random regular graphs. By approximating avalanches (cascades) as a multi-type branching process and using a generalization of Lagrange's expansion to multiple variables, we calculate the distribution of avalanche sizes within each network. Due to coupling, large avalanches in the individual networks are mitigated--in contrast to the conclusion for a ","authors_text":"Charles D. Brummitt, Elizabeth A. Leicht, Raissa M. D'Souza","cross_cats":["nlin.AO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-10-02T00:11:44Z","title":"Sandpile cascades on interacting tree-like networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0279","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:a3fce4c45e57c9a475a12d6ac39baff263335c12f0b0ce946ae387ad58f2482d","target":"record","created_at":"2026-05-18T04:39:40Z","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":"7aab31a75686ec223e6c6e8b7aa3e093b776827e056d8272b99533572f0a21da","cross_cats_sorted":["nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-10-02T00:11:44Z","title_canon_sha256":"6201dd38cd0710774c65dda22bfd979382b7ef012fd1e7e4faf2190c2b555fec"},"schema_version":"1.0","source":{"id":"1010.0279","kind":"arxiv","version":2}},"canonical_sha256":"839313e2d79887fc0d4362ccc270c8b1639b845e415abe1099b4808c2ae57f7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"839313e2d79887fc0d4362ccc270c8b1639b845e415abe1099b4808c2ae57f7d","first_computed_at":"2026-05-18T04:39:40.767702Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:40.767702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P0WdOYKS+S8zCjrErC/3DMiPKSqhhqkh4AoVX1zzwnS1oiz1jKH89ZH7c0M6VpGRNEp/wahvfqjSSPxXF05pBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:40.768238Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.0279","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3fce4c45e57c9a475a12d6ac39baff263335c12f0b0ce946ae387ad58f2482d","sha256:f6e85d9f525e01d9bcbe3409aaf9f3471dedae345388ad731b38cb64f094d1e1"],"state_sha256":"c14ec6b05400d11fc07b4ac7be451b926a5ac228b76506319700d44440d38ce0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X3auUSFRGIV3clauQFqgjKrEmVe7ouMxH4KB0SS5CAgR02HESxHuQFTw4parajOJb4pOAj6lLDcEqR8rS2psAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T06:55:13.553366Z","bundle_sha256":"e118bb44f94e834b012eba6a72fb3bb57944ee9d450384c30175e6488a9c1349"}}