{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:Q2PZZHKPX64DTXH4K2TE5C7GN3","short_pith_number":"pith:Q2PZZHKP","canonical_record":{"source":{"id":"1609.01034","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.geo-ph","submitted_at":"2016-09-05T06:30:44Z","cross_cats_sorted":[],"title_canon_sha256":"3b701e69621c74fcb59e7ed37606df68053b6cda55962f862f01fb494d8b8cbb","abstract_canon_sha256":"409c19c6e30365d9d822d3510ca597545a93f1ce714a2d56431ed102fd4956db"},"schema_version":"1.0"},"canonical_sha256":"869f9c9d4fbfb839dcfc56a64e8be66ef1cada8f4d8c5e166baebd866815c891","source":{"kind":"arxiv","id":"1609.01034","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01034","created_at":"2026-05-18T01:06:19Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01034v1","created_at":"2026-05-18T01:06:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01034","created_at":"2026-05-18T01:06:19Z"},{"alias_kind":"pith_short_12","alias_value":"Q2PZZHKPX64D","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q2PZZHKPX64DTXH4","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q2PZZHKP","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:Q2PZZHKPX64DTXH4K2TE5C7GN3","target":"record","payload":{"canonical_record":{"source":{"id":"1609.01034","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.geo-ph","submitted_at":"2016-09-05T06:30:44Z","cross_cats_sorted":[],"title_canon_sha256":"3b701e69621c74fcb59e7ed37606df68053b6cda55962f862f01fb494d8b8cbb","abstract_canon_sha256":"409c19c6e30365d9d822d3510ca597545a93f1ce714a2d56431ed102fd4956db"},"schema_version":"1.0"},"canonical_sha256":"869f9c9d4fbfb839dcfc56a64e8be66ef1cada8f4d8c5e166baebd866815c891","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:19.242522Z","signature_b64":"COH7WuVNgpI0faESWDg0GOLaXcBNdc90b6+mbpMYv0RLMPOEcp0cVxQNtKqD5qwnZCbAtBpn34QaPaGUZqxIBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"869f9c9d4fbfb839dcfc56a64e8be66ef1cada8f4d8c5e166baebd866815c891","last_reissued_at":"2026-05-18T01:06:19.241934Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:19.241934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.01034","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":"2026-05-18T01:06:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e2Zk1TF+juPlkmi60I/Caiwicto+E4AJVkTR48+DmRySG+uYotqzT0x/WkUr9egPzwOJ/E5NUCmJKs3Z+yJqAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:08:51.957291Z"},"content_sha256":"e9cf16d5bdfe894e10bf55d04a281739ac793c7457efe56ef1a2871910bf3b4a","schema_version":"1.0","event_id":"sha256:e9cf16d5bdfe894e10bf55d04a281739ac793c7457efe56ef1a2871910bf3b4a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:Q2PZZHKPX64DTXH4K2TE5C7GN3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical examination of commutativity between Backus and Gazis et al. averages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.geo-ph","authors_text":"David R. Dalton, Michael A. Slawinski","submitted_at":"2016-09-05T06:30:44Z","abstract_excerpt":"Dalton and Slawinski (2016) show that, in general, the Backus (1962) average and the Gazis et al. (1963) average do not commute. Herein, we examine the extent of this noncommutativity. We illustrate numerically that the extent of noncommutativity is a function of the strength of anisotropy. The averages nearly commute in the case of weak anisotropy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01034","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":"2026-05-18T01:06:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t3zophII54j2QYaQgr2D3U3+tx1TxAv5id6FH06gEk0z9cN/jPQsImBEP8xOzotzqMwY4xWh0re/FIxkzkX2Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:08:51.957642Z"},"content_sha256":"7aecd981ffc6898175b9d8df90379fb7177132f09d9fbec42027722b47be9b70","schema_version":"1.0","event_id":"sha256:7aecd981ffc6898175b9d8df90379fb7177132f09d9fbec42027722b47be9b70"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q2PZZHKPX64DTXH4K2TE5C7GN3/bundle.json","state_url":"https://pith.science/pith/Q2PZZHKPX64DTXH4K2TE5C7GN3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q2PZZHKPX64DTXH4K2TE5C7GN3/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":"2026-06-01T12:08:51Z","links":{"resolver":"https://pith.science/pith/Q2PZZHKPX64DTXH4K2TE5C7GN3","bundle":"https://pith.science/pith/Q2PZZHKPX64DTXH4K2TE5C7GN3/bundle.json","state":"https://pith.science/pith/Q2PZZHKPX64DTXH4K2TE5C7GN3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q2PZZHKPX64DTXH4K2TE5C7GN3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Q2PZZHKPX64DTXH4K2TE5C7GN3","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":"409c19c6e30365d9d822d3510ca597545a93f1ce714a2d56431ed102fd4956db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.geo-ph","submitted_at":"2016-09-05T06:30:44Z","title_canon_sha256":"3b701e69621c74fcb59e7ed37606df68053b6cda55962f862f01fb494d8b8cbb"},"schema_version":"1.0","source":{"id":"1609.01034","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01034","created_at":"2026-05-18T01:06:19Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01034v1","created_at":"2026-05-18T01:06:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01034","created_at":"2026-05-18T01:06:19Z"},{"alias_kind":"pith_short_12","alias_value":"Q2PZZHKPX64D","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q2PZZHKPX64DTXH4","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q2PZZHKP","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:7aecd981ffc6898175b9d8df90379fb7177132f09d9fbec42027722b47be9b70","target":"graph","created_at":"2026-05-18T01:06:19Z","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":"Dalton and Slawinski (2016) show that, in general, the Backus (1962) average and the Gazis et al. (1963) average do not commute. Herein, we examine the extent of this noncommutativity. We illustrate numerically that the extent of noncommutativity is a function of the strength of anisotropy. The averages nearly commute in the case of weak anisotropy.","authors_text":"David R. Dalton, Michael A. Slawinski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.geo-ph","submitted_at":"2016-09-05T06:30:44Z","title":"Numerical examination of commutativity between Backus and Gazis et al. averages"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01034","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:e9cf16d5bdfe894e10bf55d04a281739ac793c7457efe56ef1a2871910bf3b4a","target":"record","created_at":"2026-05-18T01:06:19Z","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":"409c19c6e30365d9d822d3510ca597545a93f1ce714a2d56431ed102fd4956db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.geo-ph","submitted_at":"2016-09-05T06:30:44Z","title_canon_sha256":"3b701e69621c74fcb59e7ed37606df68053b6cda55962f862f01fb494d8b8cbb"},"schema_version":"1.0","source":{"id":"1609.01034","kind":"arxiv","version":1}},"canonical_sha256":"869f9c9d4fbfb839dcfc56a64e8be66ef1cada8f4d8c5e166baebd866815c891","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"869f9c9d4fbfb839dcfc56a64e8be66ef1cada8f4d8c5e166baebd866815c891","first_computed_at":"2026-05-18T01:06:19.241934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:19.241934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"COH7WuVNgpI0faESWDg0GOLaXcBNdc90b6+mbpMYv0RLMPOEcp0cVxQNtKqD5qwnZCbAtBpn34QaPaGUZqxIBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:19.242522Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.01034","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9cf16d5bdfe894e10bf55d04a281739ac793c7457efe56ef1a2871910bf3b4a","sha256:7aecd981ffc6898175b9d8df90379fb7177132f09d9fbec42027722b47be9b70"],"state_sha256":"a4a8ba03163f0093804b5dcd765eaf88db27077447e0b1553d62fbe865083bfb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JYvmtDMyKb1G6Q8T20qVIoeQlhSF1DoiAPpWrpkDxXPE5qrtKTslqtxpYzYm/9pX1J7mrMiq1m8nu5twX//ODg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T12:08:51.959671Z","bundle_sha256":"3318232de65075d705a6cc7aabe936b7cd4a5052cf349a75569d0bfe68f561e4"}}