{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:NS4CG4Z5UFMTTIJBYRZ3X2UBTQ","short_pith_number":"pith:NS4CG4Z5","canonical_record":{"source":{"id":"1107.2069","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2011-07-11T16:23:35Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"f1932e27ae1ee59408d24568cfcabeb495ebd0b8c8b25c9b7897e9a117858ea5","abstract_canon_sha256":"6ffb296b554ca7fb5388a3a3c4ac47398bf3d42a4923d9f9fead65497d5cd0ce"},"schema_version":"1.0"},"canonical_sha256":"6cb823733da15939a121c473bbea819c3f31fb34e30e09ecf2950eeb1e75e875","source":{"kind":"arxiv","id":"1107.2069","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2069","created_at":"2026-05-18T03:05:45Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2069v2","created_at":"2026-05-18T03:05:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2069","created_at":"2026-05-18T03:05:45Z"},{"alias_kind":"pith_short_12","alias_value":"NS4CG4Z5UFMT","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NS4CG4Z5UFMTTIJB","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NS4CG4Z5","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:NS4CG4Z5UFMTTIJBYRZ3X2UBTQ","target":"record","payload":{"canonical_record":{"source":{"id":"1107.2069","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2011-07-11T16:23:35Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"f1932e27ae1ee59408d24568cfcabeb495ebd0b8c8b25c9b7897e9a117858ea5","abstract_canon_sha256":"6ffb296b554ca7fb5388a3a3c4ac47398bf3d42a4923d9f9fead65497d5cd0ce"},"schema_version":"1.0"},"canonical_sha256":"6cb823733da15939a121c473bbea819c3f31fb34e30e09ecf2950eeb1e75e875","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:45.065348Z","signature_b64":"aOCVYmsjfCNHA4oXtMzKrXjDnzAahlAg8S2phYiIHp4aBq+5uHrYWpfkjSOgomMHO4KN5O1Bc9GM5hHOB9RTAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cb823733da15939a121c473bbea819c3f31fb34e30e09ecf2950eeb1e75e875","last_reissued_at":"2026-05-18T03:05:45.064814Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:45.064814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.2069","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":"2026-05-18T03:05:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Ihm2bJaneWk62C0Rbr1cWO8kM5Wviilx0X6xcyX+j70Hab4GKk8F3WNWFxFf5aC5JsfdYUpF4eL4JDqNhWHCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:37:00.501644Z"},"content_sha256":"0617cfb2db20c59d98af5a48d66de21861e1cf90643894ae40a0eff7144f7981","schema_version":"1.0","event_id":"sha256:0617cfb2db20c59d98af5a48d66de21861e1cf90643894ae40a0eff7144f7981"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:NS4CG4Z5UFMTTIJBYRZ3X2UBTQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Influence of polydispersity on micromechanics of granular materials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.soft","authors_text":"Dietrich E. Wolf, Mahyar Madadi, M. Reza Shaebani, Stefan Luding","submitted_at":"2011-07-11T16:23:35Z","abstract_excerpt":"We study the effect of polydispersity on the macroscopic physical properties of granular packings in two and three dimensions. A mean-field approach is developed to approximate the macroscale quantities as functions of the microscopic ones. We show that the trace of the fabric and stress tensors are proportional to the mean packing properties (e.g. packing fraction, average coordination number, and average normal force) and dimensionless correction factors, which depend only on the moments of the particle-size distribution. Similar results are obtained for the elements of the stiffness tensor "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2069","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":"2026-05-18T03:05:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jDG3kVdl3mABjKxOqGp/A6/gW2rcSMIPShI4fi28HkiKY2z2TfJL4MGZDmtLvengD/y1CCEEv7eOO9yEzwA1CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:37:00.501991Z"},"content_sha256":"0e66f36a9284af74b3f84f3e31cce719c8f79e743ade2c6f3fe1c79fe9c3594b","schema_version":"1.0","event_id":"sha256:0e66f36a9284af74b3f84f3e31cce719c8f79e743ade2c6f3fe1c79fe9c3594b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NS4CG4Z5UFMTTIJBYRZ3X2UBTQ/bundle.json","state_url":"https://pith.science/pith/NS4CG4Z5UFMTTIJBYRZ3X2UBTQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NS4CG4Z5UFMTTIJBYRZ3X2UBTQ/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":"2026-06-03T10:37:00Z","links":{"resolver":"https://pith.science/pith/NS4CG4Z5UFMTTIJBYRZ3X2UBTQ","bundle":"https://pith.science/pith/NS4CG4Z5UFMTTIJBYRZ3X2UBTQ/bundle.json","state":"https://pith.science/pith/NS4CG4Z5UFMTTIJBYRZ3X2UBTQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NS4CG4Z5UFMTTIJBYRZ3X2UBTQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NS4CG4Z5UFMTTIJBYRZ3X2UBTQ","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":"6ffb296b554ca7fb5388a3a3c4ac47398bf3d42a4923d9f9fead65497d5cd0ce","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2011-07-11T16:23:35Z","title_canon_sha256":"f1932e27ae1ee59408d24568cfcabeb495ebd0b8c8b25c9b7897e9a117858ea5"},"schema_version":"1.0","source":{"id":"1107.2069","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2069","created_at":"2026-05-18T03:05:45Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2069v2","created_at":"2026-05-18T03:05:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2069","created_at":"2026-05-18T03:05:45Z"},{"alias_kind":"pith_short_12","alias_value":"NS4CG4Z5UFMT","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NS4CG4Z5UFMTTIJB","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NS4CG4Z5","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:0e66f36a9284af74b3f84f3e31cce719c8f79e743ade2c6f3fe1c79fe9c3594b","target":"graph","created_at":"2026-05-18T03:05:45Z","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":"We study the effect of polydispersity on the macroscopic physical properties of granular packings in two and three dimensions. A mean-field approach is developed to approximate the macroscale quantities as functions of the microscopic ones. We show that the trace of the fabric and stress tensors are proportional to the mean packing properties (e.g. packing fraction, average coordination number, and average normal force) and dimensionless correction factors, which depend only on the moments of the particle-size distribution. Similar results are obtained for the elements of the stiffness tensor ","authors_text":"Dietrich E. Wolf, Mahyar Madadi, M. Reza Shaebani, Stefan Luding","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2011-07-11T16:23:35Z","title":"Influence of polydispersity on micromechanics of granular materials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2069","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":"sha256:0617cfb2db20c59d98af5a48d66de21861e1cf90643894ae40a0eff7144f7981","target":"record","created_at":"2026-05-18T03:05:45Z","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":"6ffb296b554ca7fb5388a3a3c4ac47398bf3d42a4923d9f9fead65497d5cd0ce","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2011-07-11T16:23:35Z","title_canon_sha256":"f1932e27ae1ee59408d24568cfcabeb495ebd0b8c8b25c9b7897e9a117858ea5"},"schema_version":"1.0","source":{"id":"1107.2069","kind":"arxiv","version":2}},"canonical_sha256":"6cb823733da15939a121c473bbea819c3f31fb34e30e09ecf2950eeb1e75e875","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cb823733da15939a121c473bbea819c3f31fb34e30e09ecf2950eeb1e75e875","first_computed_at":"2026-05-18T03:05:45.064814Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:45.064814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aOCVYmsjfCNHA4oXtMzKrXjDnzAahlAg8S2phYiIHp4aBq+5uHrYWpfkjSOgomMHO4KN5O1Bc9GM5hHOB9RTAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:45.065348Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.2069","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0617cfb2db20c59d98af5a48d66de21861e1cf90643894ae40a0eff7144f7981","sha256:0e66f36a9284af74b3f84f3e31cce719c8f79e743ade2c6f3fe1c79fe9c3594b"],"state_sha256":"c66378a2d50e9e795bedcbc5e0ed2c02e83bb71add828485af86926264940315"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TSFrSW5+8JeQn9uIVYeiWRRBgEAJXI2mNbmAs/57PT8CPFpL07xbuKETX8wJrJpxVUCGWdNmfXYezES9nTHMBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T10:37:00.503920Z","bundle_sha256":"6dae7e5af4e41a4159fbf937d215a22f2c867188d67c09958d5bddf9be6be1a3"}}