{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:AVZBED56PFNYPJ6CRQMIXWB3QF","short_pith_number":"pith:AVZBED56","canonical_record":{"source":{"id":"1009.0601","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-09-03T08:18:34Z","cross_cats_sorted":[],"title_canon_sha256":"36f02869b5ae1d3bba6359be67927a983563faa1e22f6a7be41c20d7f0f7404c","abstract_canon_sha256":"c26c31ee9a8984aaf00e255e6ee2950dc45fd4ce8d211dbc8eb102013baf6bab"},"schema_version":"1.0"},"canonical_sha256":"0572120fbe795b87a7c28c188bd83b8158d289d77541aa7bff33101df68a780e","source":{"kind":"arxiv","id":"1009.0601","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.0601","created_at":"2026-05-18T04:37:12Z"},{"alias_kind":"arxiv_version","alias_value":"1009.0601v2","created_at":"2026-05-18T04:37:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0601","created_at":"2026-05-18T04:37:12Z"},{"alias_kind":"pith_short_12","alias_value":"AVZBED56PFNY","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AVZBED56PFNYPJ6C","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AVZBED56","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:AVZBED56PFNYPJ6CRQMIXWB3QF","target":"record","payload":{"canonical_record":{"source":{"id":"1009.0601","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-09-03T08:18:34Z","cross_cats_sorted":[],"title_canon_sha256":"36f02869b5ae1d3bba6359be67927a983563faa1e22f6a7be41c20d7f0f7404c","abstract_canon_sha256":"c26c31ee9a8984aaf00e255e6ee2950dc45fd4ce8d211dbc8eb102013baf6bab"},"schema_version":"1.0"},"canonical_sha256":"0572120fbe795b87a7c28c188bd83b8158d289d77541aa7bff33101df68a780e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:37:12.647022Z","signature_b64":"Wg0vcEbOgVm7nyRa+CzCRGe82+/Lo5SesPDxknQLU3LmZjgz+7vgwrjt217s5AMkUxKhWDrrOKyriAfwrrx9Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0572120fbe795b87a7c28c188bd83b8158d289d77541aa7bff33101df68a780e","last_reissued_at":"2026-05-18T04:37:12.646310Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:37:12.646310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.0601","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":"2026-05-18T04:37:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oj3I/uFqUCiLU/N2NA8obGXJkISzRqf/bWXX1G6r/i14qxIfarOlU2CgIrSZEHBk+zpv76eQZdpjEyjtLcS8CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:06:07.620704Z"},"content_sha256":"cb45ab7458941ede1af6eda611962018d0a2c041206a2ade6c2545513ebaae4b","schema_version":"1.0","event_id":"sha256:cb45ab7458941ede1af6eda611962018d0a2c041206a2ade6c2545513ebaae4b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:AVZBED56PFNYPJ6CRQMIXWB3QF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local Anisotropy of Fluids using Minkowski Tensors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Christian Goll, Fabian M. Schaller, Gerd E. Schr\\\"oder-Turk, Klaus Mecke, Markus Spanner, Nobuyasu Ito, Sebastian C. Kapfer, Tomoaki Nogawa, Walter Mickel","submitted_at":"2010-09-03T08:18:34Z","abstract_excerpt":"Statistics of the free volume available to individual particles have previously been studied for simple and complex fluids, granular matter, amorphous solids, and structural glasses. Minkowski tensors provide a set of shape measures that are based on strong mathematical theorems and easily computed for polygonal and polyhedral bodies such as free volume cells (Voronoi cells). They characterize the local structure beyond the two-point correlation function and are suitable to define indices $0\\leq \\beta_\\nu^{a,b}\\leq 1$ of local anisotropy. Here, we analyze the statistics of Minkowski tensors fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0601","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":"2026-05-18T04:37:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HGPP19q3WzKa17EpgITiat0yzx+Ct2gfBS3OnIl2kCsxVKiW+GVSs103mUpoGxMpW6nR2wZSuK6BiVwC9thsDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:06:07.621394Z"},"content_sha256":"e1261b51a8dc5371dbe251186c199ab6aba71f45a4091e907989fa8689cc6217","schema_version":"1.0","event_id":"sha256:e1261b51a8dc5371dbe251186c199ab6aba71f45a4091e907989fa8689cc6217"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AVZBED56PFNYPJ6CRQMIXWB3QF/bundle.json","state_url":"https://pith.science/pith/AVZBED56PFNYPJ6CRQMIXWB3QF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AVZBED56PFNYPJ6CRQMIXWB3QF/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":"2026-05-27T04:06:07Z","links":{"resolver":"https://pith.science/pith/AVZBED56PFNYPJ6CRQMIXWB3QF","bundle":"https://pith.science/pith/AVZBED56PFNYPJ6CRQMIXWB3QF/bundle.json","state":"https://pith.science/pith/AVZBED56PFNYPJ6CRQMIXWB3QF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AVZBED56PFNYPJ6CRQMIXWB3QF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:AVZBED56PFNYPJ6CRQMIXWB3QF","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":"c26c31ee9a8984aaf00e255e6ee2950dc45fd4ce8d211dbc8eb102013baf6bab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-09-03T08:18:34Z","title_canon_sha256":"36f02869b5ae1d3bba6359be67927a983563faa1e22f6a7be41c20d7f0f7404c"},"schema_version":"1.0","source":{"id":"1009.0601","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.0601","created_at":"2026-05-18T04:37:12Z"},{"alias_kind":"arxiv_version","alias_value":"1009.0601v2","created_at":"2026-05-18T04:37:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0601","created_at":"2026-05-18T04:37:12Z"},{"alias_kind":"pith_short_12","alias_value":"AVZBED56PFNY","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AVZBED56PFNYPJ6C","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AVZBED56","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:e1261b51a8dc5371dbe251186c199ab6aba71f45a4091e907989fa8689cc6217","target":"graph","created_at":"2026-05-18T04:37:12Z","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":"Statistics of the free volume available to individual particles have previously been studied for simple and complex fluids, granular matter, amorphous solids, and structural glasses. Minkowski tensors provide a set of shape measures that are based on strong mathematical theorems and easily computed for polygonal and polyhedral bodies such as free volume cells (Voronoi cells). They characterize the local structure beyond the two-point correlation function and are suitable to define indices $0\\leq \\beta_\\nu^{a,b}\\leq 1$ of local anisotropy. Here, we analyze the statistics of Minkowski tensors fo","authors_text":"Christian Goll, Fabian M. Schaller, Gerd E. Schr\\\"oder-Turk, Klaus Mecke, Markus Spanner, Nobuyasu Ito, Sebastian C. Kapfer, Tomoaki Nogawa, Walter Mickel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-09-03T08:18:34Z","title":"Local Anisotropy of Fluids using Minkowski Tensors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0601","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:cb45ab7458941ede1af6eda611962018d0a2c041206a2ade6c2545513ebaae4b","target":"record","created_at":"2026-05-18T04:37:12Z","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":"c26c31ee9a8984aaf00e255e6ee2950dc45fd4ce8d211dbc8eb102013baf6bab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-09-03T08:18:34Z","title_canon_sha256":"36f02869b5ae1d3bba6359be67927a983563faa1e22f6a7be41c20d7f0f7404c"},"schema_version":"1.0","source":{"id":"1009.0601","kind":"arxiv","version":2}},"canonical_sha256":"0572120fbe795b87a7c28c188bd83b8158d289d77541aa7bff33101df68a780e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0572120fbe795b87a7c28c188bd83b8158d289d77541aa7bff33101df68a780e","first_computed_at":"2026-05-18T04:37:12.646310Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:37:12.646310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wg0vcEbOgVm7nyRa+CzCRGe82+/Lo5SesPDxknQLU3LmZjgz+7vgwrjt217s5AMkUxKhWDrrOKyriAfwrrx9Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:37:12.647022Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.0601","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb45ab7458941ede1af6eda611962018d0a2c041206a2ade6c2545513ebaae4b","sha256:e1261b51a8dc5371dbe251186c199ab6aba71f45a4091e907989fa8689cc6217"],"state_sha256":"4da2050390802e4cf4a0cca4af87b80ee4249db958499d31d4a21fb377c72370"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ad52uJNvsW/p0dG3PI84DEINrhStKvkfyLTGrjHmxusdnKpCCCTfM/BrMCqILLHsGTcljUvTvPtTD+vqOHYNAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T04:06:07.623984Z","bundle_sha256":"caa3e22607ca2c1bb15d677f8e01f6876b813e87ddf57acd09bea132f8fd5ff7"}}