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Tuning the value of $\\beta$ continuously over a wide range, the critical behavior of the fiber bundle has been studied both analytically as well as numerically. Our results are: (i) The critical load $\\sigma_c(\\beta,N)$ for the bundle of size $N$ approaches its asymptotic value $\\sigma_c(\\beta)$ as $\\sigma_c(\\beta,N) = \\sigma_c(\\beta)+AN^{-1/\\nu(\\beta)"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1502.05143","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-02-18T07:38:05Z","cross_cats_sorted":[],"title_canon_sha256":"bcfb4b4e832282c268b58a694e992b1f0015d2e61829c0ab6656b583259a1735","abstract_canon_sha256":"e5c5f72d59eadd9ca53e00aa735eea384fe9f479e234d0c4cc3d6f98b5825918"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:54.127166Z","signature_b64":"F/j1riR+T5C8K0VHhIx3d9AqW4A6UCQsS0DxwtneqTRYIWm+HIqgMKAnp55v6EiGfiJeOChkGJLC00JerfxGBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92380393bd3f75702e05087ad2b2afc98e46ed1dac166c8db892623d84c622d3","last_reissued_at":"2026-05-17T23:42:54.126534Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:54.126534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fiber Bundle model with Highly Disordered Breaking Thresholds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Chandreyee Roy, S. 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Our results are: (i) The critical load $\\sigma_c(\\beta,N)$ for the bundle of size $N$ approaches its asymptotic value $\\sigma_c(\\beta)$ as $\\sigma_c(\\beta,N) = \\sigma_c(\\beta)+AN^{-1/\\nu(\\beta)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05143","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1502.05143","created_at":"2026-05-17T23:42:54.126632+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.05143v1","created_at":"2026-05-17T23:42:54.126632+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05143","created_at":"2026-05-17T23:42:54.126632+00:00"},{"alias_kind":"pith_short_12","alias_value":"SI4AHE55H52X","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"SI4AHE55H52XALQF","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"SI4AHE55","created_at":"2026-05-18T12:29:42.218222+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SI4AHE55H52XALQFBB5NFMVPZG","json":"https://pith.science/pith/SI4AHE55H52XALQFBB5NFMVPZG.json","graph_json":"https://pith.science/api/pith-number/SI4AHE55H52XALQFBB5NFMVPZG/graph.json","events_json":"https://pith.science/api/pith-number/SI4AHE55H52XALQFBB5NFMVPZG/events.json","paper":"https://pith.science/paper/SI4AHE55"},"agent_actions":{"view_html":"https://pith.science/pith/SI4AHE55H52XALQFBB5NFMVPZG","download_json":"https://pith.science/pith/SI4AHE55H52XALQFBB5NFMVPZG.json","view_paper":"https://pith.science/paper/SI4AHE55","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.05143&json=true","fetch_graph":"https://pith.science/api/pith-number/SI4AHE55H52XALQFBB5NFMVPZG/graph.json","fetch_events":"https://pith.science/api/pith-number/SI4AHE55H52XALQFBB5NFMVPZG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SI4AHE55H52XALQFBB5NFMVPZG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SI4AHE55H52XALQFBB5NFMVPZG/action/storage_attestation","attest_author":"https://pith.science/pith/SI4AHE55H52XALQFBB5NFMVPZG/action/author_attestation","sign_citation":"https://pith.science/pith/SI4AHE55H52XALQFBB5NFMVPZG/action/citation_signature","submit_replication":"https://pith.science/pith/SI4AHE55H52XALQFBB5NFMVPZG/action/replication_record"}},"created_at":"2026-05-17T23:42:54.126632+00:00","updated_at":"2026-05-17T23:42:54.126632+00:00"}