{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:TQCHCZL2JKPSC6EFR2EAQZDLA3","short_pith_number":"pith:TQCHCZL2","canonical_record":{"source":{"id":"1210.3701","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-10-13T12:18:52Z","cross_cats_sorted":["math.MP","physics.class-ph"],"title_canon_sha256":"9277da5e0db3a6e32aaf9a640f1367b5580053fb1deea95036c816780e041134","abstract_canon_sha256":"ef050273643513d9508bad3e72a0f58bf37bc04f657a3781df35e83435d42921"},"schema_version":"1.0"},"canonical_sha256":"9c0471657a4a9f2178858e8808646b06dce9b9fe5a768f62ac1cc7ab60e4bb1a","source":{"kind":"arxiv","id":"1210.3701","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3701","created_at":"2026-05-18T01:53:55Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3701v1","created_at":"2026-05-18T01:53:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3701","created_at":"2026-05-18T01:53:55Z"},{"alias_kind":"pith_short_12","alias_value":"TQCHCZL2JKPS","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TQCHCZL2JKPSC6EF","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TQCHCZL2","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:TQCHCZL2JKPSC6EFR2EAQZDLA3","target":"record","payload":{"canonical_record":{"source":{"id":"1210.3701","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-10-13T12:18:52Z","cross_cats_sorted":["math.MP","physics.class-ph"],"title_canon_sha256":"9277da5e0db3a6e32aaf9a640f1367b5580053fb1deea95036c816780e041134","abstract_canon_sha256":"ef050273643513d9508bad3e72a0f58bf37bc04f657a3781df35e83435d42921"},"schema_version":"1.0"},"canonical_sha256":"9c0471657a4a9f2178858e8808646b06dce9b9fe5a768f62ac1cc7ab60e4bb1a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:53:55.797773Z","signature_b64":"yeq7pg0C4k6zIHMwnS7+8G+a9MINWIN3l5AAadsiyP5qsoBcb7QOMBv2QGTV68FS32tDGAYenSq8JppFcegiCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c0471657a4a9f2178858e8808646b06dce9b9fe5a768f62ac1cc7ab60e4bb1a","last_reissued_at":"2026-05-18T01:53:55.797031Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:53:55.797031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.3701","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":"2026-05-18T01:53:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n56Ul5xezPCvrCDPyuKfAjqXhXnimXHa7h1fVFi3WVUQXg7w+2ISFfhAewFnMiPd1BFYnbWmmE9ybNueFdYQDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T23:20:07.186492Z"},"content_sha256":"1cf875ef31c5820aec9ea4e1a2b8ee84072cfa9203e849063cdd486b310fac3b","schema_version":"1.0","event_id":"sha256:1cf875ef31c5820aec9ea4e1a2b8ee84072cfa9203e849063cdd486b310fac3b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:TQCHCZL2JKPSC6EFR2EAQZDLA3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Predicting the pressure-volume curve of an elastic microsphere composite","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","physics.class-ph"],"primary_cat":"math-ph","authors_text":"I. David Abrahams, Riccardo De Pascalis, William J. Parnell","submitted_at":"2012-10-13T12:18:52Z","abstract_excerpt":"The effective macroscopic response of nonlinear elastomeric inhomogeneous materials is of great interest in many applications including nonlinear composite materials and soft biological tissues. The interest of the present work is associated with a microsphere composite material, which is modelled as a matrix-inclusion composite. The matrix phase is a homogeneous isotropic nonlinear rubber-like material and the inclusion phase is more complex, consisting of a distribution of sizes of stiff thin spherical shells filled with gas. Experimentally, such materials have been shown to undergo complex "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3701","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":"2026-05-18T01:53:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zm1WaH6+OMg3rkHhdynRLPvqE9jDK/UG1xOhxUS8gUaloeyjWa/IisN4xCzxCEMscSg8F0IvIz3u0TFdvfU7Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T23:20:07.186879Z"},"content_sha256":"5d7add96428b48e98f0d40e45661f5a1a86f288820d4a1477121c46cacc926d4","schema_version":"1.0","event_id":"sha256:5d7add96428b48e98f0d40e45661f5a1a86f288820d4a1477121c46cacc926d4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TQCHCZL2JKPSC6EFR2EAQZDLA3/bundle.json","state_url":"https://pith.science/pith/TQCHCZL2JKPSC6EFR2EAQZDLA3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TQCHCZL2JKPSC6EFR2EAQZDLA3/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":"2026-06-20T23:20:07Z","links":{"resolver":"https://pith.science/pith/TQCHCZL2JKPSC6EFR2EAQZDLA3","bundle":"https://pith.science/pith/TQCHCZL2JKPSC6EFR2EAQZDLA3/bundle.json","state":"https://pith.science/pith/TQCHCZL2JKPSC6EFR2EAQZDLA3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TQCHCZL2JKPSC6EFR2EAQZDLA3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TQCHCZL2JKPSC6EFR2EAQZDLA3","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":"ef050273643513d9508bad3e72a0f58bf37bc04f657a3781df35e83435d42921","cross_cats_sorted":["math.MP","physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-10-13T12:18:52Z","title_canon_sha256":"9277da5e0db3a6e32aaf9a640f1367b5580053fb1deea95036c816780e041134"},"schema_version":"1.0","source":{"id":"1210.3701","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3701","created_at":"2026-05-18T01:53:55Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3701v1","created_at":"2026-05-18T01:53:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3701","created_at":"2026-05-18T01:53:55Z"},{"alias_kind":"pith_short_12","alias_value":"TQCHCZL2JKPS","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TQCHCZL2JKPSC6EF","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TQCHCZL2","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:5d7add96428b48e98f0d40e45661f5a1a86f288820d4a1477121c46cacc926d4","target":"graph","created_at":"2026-05-18T01:53:55Z","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":"The effective macroscopic response of nonlinear elastomeric inhomogeneous materials is of great interest in many applications including nonlinear composite materials and soft biological tissues. The interest of the present work is associated with a microsphere composite material, which is modelled as a matrix-inclusion composite. The matrix phase is a homogeneous isotropic nonlinear rubber-like material and the inclusion phase is more complex, consisting of a distribution of sizes of stiff thin spherical shells filled with gas. Experimentally, such materials have been shown to undergo complex ","authors_text":"I. David Abrahams, Riccardo De Pascalis, William J. Parnell","cross_cats":["math.MP","physics.class-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-10-13T12:18:52Z","title":"Predicting the pressure-volume curve of an elastic microsphere composite"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3701","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":"sha256:1cf875ef31c5820aec9ea4e1a2b8ee84072cfa9203e849063cdd486b310fac3b","target":"record","created_at":"2026-05-18T01:53:55Z","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":"ef050273643513d9508bad3e72a0f58bf37bc04f657a3781df35e83435d42921","cross_cats_sorted":["math.MP","physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-10-13T12:18:52Z","title_canon_sha256":"9277da5e0db3a6e32aaf9a640f1367b5580053fb1deea95036c816780e041134"},"schema_version":"1.0","source":{"id":"1210.3701","kind":"arxiv","version":1}},"canonical_sha256":"9c0471657a4a9f2178858e8808646b06dce9b9fe5a768f62ac1cc7ab60e4bb1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c0471657a4a9f2178858e8808646b06dce9b9fe5a768f62ac1cc7ab60e4bb1a","first_computed_at":"2026-05-18T01:53:55.797031Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:53:55.797031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yeq7pg0C4k6zIHMwnS7+8G+a9MINWIN3l5AAadsiyP5qsoBcb7QOMBv2QGTV68FS32tDGAYenSq8JppFcegiCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:53:55.797773Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.3701","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cf875ef31c5820aec9ea4e1a2b8ee84072cfa9203e849063cdd486b310fac3b","sha256:5d7add96428b48e98f0d40e45661f5a1a86f288820d4a1477121c46cacc926d4"],"state_sha256":"eede54efe47491da1f5ac4283e2da8670995990237d00b64432e8ea45182de09"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kX5TySvJN7nmKdhv666CFOOvsQB041NABmulksrotPonpV7c/H4duIEOqLDApyueS9eBZ4YSloNunqzeoumJDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T23:20:07.188926Z","bundle_sha256":"4b9bf4b166cfc907ba7d4e0530f02a7f520590267457f5822535fa65befcdaa4"}}