{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:FZUHSDJLKZPWF4M675OGYCXYEE","short_pith_number":"pith:FZUHSDJL","canonical_record":{"source":{"id":"cond-mat/0409045","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.other","submitted_at":"2004-09-02T08:49:44Z","cross_cats_sorted":[],"title_canon_sha256":"4acbb5c5b86af68a756b4a90fb25fb683645538f175fbb6ea77b14731bf0a5b3","abstract_canon_sha256":"49df0ba8d4f627afc80d05e0b1c0199c58e369c2ffeef2b5cbff95610d457cf4"},"schema_version":"1.0"},"canonical_sha256":"2e68790d2b565f62f19eff5c6c0af8210c6414672ee031f93488c9d8273f32cd","source":{"kind":"arxiv","id":"cond-mat/0409045","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0409045","created_at":"2026-05-18T01:39:57Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0409045v1","created_at":"2026-05-18T01:39:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0409045","created_at":"2026-05-18T01:39:57Z"},{"alias_kind":"pith_short_12","alias_value":"FZUHSDJLKZPW","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"FZUHSDJLKZPWF4M6","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"FZUHSDJL","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:FZUHSDJLKZPWF4M675OGYCXYEE","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0409045","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.other","submitted_at":"2004-09-02T08:49:44Z","cross_cats_sorted":[],"title_canon_sha256":"4acbb5c5b86af68a756b4a90fb25fb683645538f175fbb6ea77b14731bf0a5b3","abstract_canon_sha256":"49df0ba8d4f627afc80d05e0b1c0199c58e369c2ffeef2b5cbff95610d457cf4"},"schema_version":"1.0"},"canonical_sha256":"2e68790d2b565f62f19eff5c6c0af8210c6414672ee031f93488c9d8273f32cd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:57.787954Z","signature_b64":"WRQzUneBVdyUd5cFGXfqufsCpDqCUWMaCl+0kdmQN/BGmehm2o5W3WXiTUAGBjIIhBxSH7d7MlQL0OvvpP2FAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e68790d2b565f62f19eff5c6c0af8210c6414672ee031f93488c9d8273f32cd","last_reissued_at":"2026-05-18T01:39:57.787467Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:57.787467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0409045","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":"2026-05-18T01:39:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zG4o4uV1XPbTAPJXaJAqX+xTgbLy/MOODmtQs+zyPEAoMTtWd4mnAAnB4HYlB4gWRj5ceOUCqGCI7MjyjHkBAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:23:48.981580Z"},"content_sha256":"832607157fa9521f3f92eebc559a537c15514c848b29fcafca6fe022cde43312","schema_version":"1.0","event_id":"sha256:832607157fa9521f3f92eebc559a537c15514c848b29fcafca6fe022cde43312"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:FZUHSDJLKZPWF4M675OGYCXYEE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Effective toughness of heterogeneous brittle materials","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.other","authors_text":"Damien Vandembroucq (SVI), Francois Hild (LMT), Stephane Roux (SVI)","submitted_at":"2004-09-02T08:49:44Z","abstract_excerpt":"A heterogeneous brittle material characterized by a random field of local toughness Kc(x) can be represented by an equivalent homogeneous medium of toughness, Keff. Homogenization refers to a process of estimating Keff from the local field Kc(x). An approach based on a perturbative expansion of the stress intensity factor along a rough crack front shows the occurrence of different regimes depending on the correlation length of the local toughness field in the direction of crack propagation. A `\"weak pinning\" regime takes place for long correlation lengths, where the effective toughness is the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0409045","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":"2026-05-18T01:39:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GSRsmrPfvGwu3rA7/b25nENM/NDWvVAOv8qDEPjsW9uWun7Vzo8lYeWRet7L+sIoWiy/3j8ERTmTtqRhAgpZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:23:48.982239Z"},"content_sha256":"24a410f4870d13864244d558ec43964c22dedf27697e59e89c288547279ed6ae","schema_version":"1.0","event_id":"sha256:24a410f4870d13864244d558ec43964c22dedf27697e59e89c288547279ed6ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FZUHSDJLKZPWF4M675OGYCXYEE/bundle.json","state_url":"https://pith.science/pith/FZUHSDJLKZPWF4M675OGYCXYEE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FZUHSDJLKZPWF4M675OGYCXYEE/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":"2026-05-27T18:23:48Z","links":{"resolver":"https://pith.science/pith/FZUHSDJLKZPWF4M675OGYCXYEE","bundle":"https://pith.science/pith/FZUHSDJLKZPWF4M675OGYCXYEE/bundle.json","state":"https://pith.science/pith/FZUHSDJLKZPWF4M675OGYCXYEE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FZUHSDJLKZPWF4M675OGYCXYEE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:FZUHSDJLKZPWF4M675OGYCXYEE","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":"49df0ba8d4f627afc80d05e0b1c0199c58e369c2ffeef2b5cbff95610d457cf4","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.other","submitted_at":"2004-09-02T08:49:44Z","title_canon_sha256":"4acbb5c5b86af68a756b4a90fb25fb683645538f175fbb6ea77b14731bf0a5b3"},"schema_version":"1.0","source":{"id":"cond-mat/0409045","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0409045","created_at":"2026-05-18T01:39:57Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0409045v1","created_at":"2026-05-18T01:39:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0409045","created_at":"2026-05-18T01:39:57Z"},{"alias_kind":"pith_short_12","alias_value":"FZUHSDJLKZPW","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"FZUHSDJLKZPWF4M6","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"FZUHSDJL","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:24a410f4870d13864244d558ec43964c22dedf27697e59e89c288547279ed6ae","target":"graph","created_at":"2026-05-18T01:39:57Z","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 heterogeneous brittle material characterized by a random field of local toughness Kc(x) can be represented by an equivalent homogeneous medium of toughness, Keff. Homogenization refers to a process of estimating Keff from the local field Kc(x). An approach based on a perturbative expansion of the stress intensity factor along a rough crack front shows the occurrence of different regimes depending on the correlation length of the local toughness field in the direction of crack propagation. A `\"weak pinning\" regime takes place for long correlation lengths, where the effective toughness is the ","authors_text":"Damien Vandembroucq (SVI), Francois Hild (LMT), Stephane Roux (SVI)","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.other","submitted_at":"2004-09-02T08:49:44Z","title":"Effective toughness of heterogeneous brittle materials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0409045","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":"sha256:832607157fa9521f3f92eebc559a537c15514c848b29fcafca6fe022cde43312","target":"record","created_at":"2026-05-18T01:39:57Z","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":"49df0ba8d4f627afc80d05e0b1c0199c58e369c2ffeef2b5cbff95610d457cf4","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.other","submitted_at":"2004-09-02T08:49:44Z","title_canon_sha256":"4acbb5c5b86af68a756b4a90fb25fb683645538f175fbb6ea77b14731bf0a5b3"},"schema_version":"1.0","source":{"id":"cond-mat/0409045","kind":"arxiv","version":1}},"canonical_sha256":"2e68790d2b565f62f19eff5c6c0af8210c6414672ee031f93488c9d8273f32cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e68790d2b565f62f19eff5c6c0af8210c6414672ee031f93488c9d8273f32cd","first_computed_at":"2026-05-18T01:39:57.787467Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:57.787467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WRQzUneBVdyUd5cFGXfqufsCpDqCUWMaCl+0kdmQN/BGmehm2o5W3WXiTUAGBjIIhBxSH7d7MlQL0OvvpP2FAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:57.787954Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0409045","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:832607157fa9521f3f92eebc559a537c15514c848b29fcafca6fe022cde43312","sha256:24a410f4870d13864244d558ec43964c22dedf27697e59e89c288547279ed6ae"],"state_sha256":"06d05798629f473e780f36e12b43b02cee8677bee3ec739c3d5e65f6655890e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"980jvKwgKZ3tAyCGzdFZ+rfuYdrpC42poaq/m0GrHXLon2vey8k5yBA89xBaGk1UrJDI/DG+ZIYTwuoSPrfaDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T18:23:48.986126Z","bundle_sha256":"cf690cc104862ebc518e8c5517a1cbf4b02289eebc00180d8da1382988e311c1"}}