{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:GB4BDAAJZ3BUJNR64PVFHXE7PL","short_pith_number":"pith:GB4BDAAJ","canonical_record":{"source":{"id":"1803.06106","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2018-03-16T08:00:46Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"6f7a5cae022ff18abb93e4a42d9853a9f8e2cd12d259f8079a09283e96474bf0","abstract_canon_sha256":"863c145eb49b9a25415fc61da69e9b275bd0f091a83f301ebd7d58ed9ec0949d"},"schema_version":"1.0"},"canonical_sha256":"3078118009cec344b63ee3ea53dc9f7ad8d5c34a0d2f5aba63b33f8cf13135ab","source":{"kind":"arxiv","id":"1803.06106","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.06106","created_at":"2026-05-18T00:02:12Z"},{"alias_kind":"arxiv_version","alias_value":"1803.06106v2","created_at":"2026-05-18T00:02:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.06106","created_at":"2026-05-18T00:02:12Z"},{"alias_kind":"pith_short_12","alias_value":"GB4BDAAJZ3BU","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GB4BDAAJZ3BUJNR6","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GB4BDAAJ","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:GB4BDAAJZ3BUJNR64PVFHXE7PL","target":"record","payload":{"canonical_record":{"source":{"id":"1803.06106","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2018-03-16T08:00:46Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"6f7a5cae022ff18abb93e4a42d9853a9f8e2cd12d259f8079a09283e96474bf0","abstract_canon_sha256":"863c145eb49b9a25415fc61da69e9b275bd0f091a83f301ebd7d58ed9ec0949d"},"schema_version":"1.0"},"canonical_sha256":"3078118009cec344b63ee3ea53dc9f7ad8d5c34a0d2f5aba63b33f8cf13135ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:12.664040Z","signature_b64":"IeH1gsD13IuF0qkUCvXkvnb56tBX8r31Utw+w1mOH4RnyybCA12ajyaAr+KEOAkyl1fa4dAOF/V2ZFraTs6UDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3078118009cec344b63ee3ea53dc9f7ad8d5c34a0d2f5aba63b33f8cf13135ab","last_reissued_at":"2026-05-18T00:02:12.663292Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:12.663292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.06106","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":"2026-05-18T00:02:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AV1siMmBzbinwcrfrk4u3Os0Ikqt64Vyp3Cp+AL5aed/rOEwqT51/tktebxNQSttSSfOfdbEuTkMDplsYjxiAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:11:07.586860Z"},"content_sha256":"2fe637527b0dd1f9ca178f2c037c4908e4197d3596f625aeb7769ce36abd1bd6","schema_version":"1.0","event_id":"sha256:2fe637527b0dd1f9ca178f2c037c4908e4197d3596f625aeb7769ce36abd1bd6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:GB4BDAAJZ3BUJNR64PVFHXE7PL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Irreducible Polynomial Functional Basis of Two-dimensional Eshelby Tensors","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Liping Zhang, Yannan Chen, Zhenyu Ming","submitted_at":"2018-03-16T08:00:46Z","abstract_excerpt":"Representation theorems for both isotropic and anisotropic functions are of prime importance in both theoretical and applied mechanics. The Eshelby inclusion problem is very fundamental, and is of particular importance in the design of advanced functional composite materials. In this paper, we discuss about two-dimensional Eshelby tensors (denoted as $M^{(2)}$). Eshelby tensors satisfy the minor index symmetry $M_{ijkl}^{(2)}=M_{jikl}^{(2)}=M_{ijlk}^{(2)}$ and have wide applications in many fields of mechanics. In view of the representation of two-dimensional irreducible tensors in complex fie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06106","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":"2026-05-18T00:02:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+cWZWuskAotet9Vyo7ZYDuNaETNzd31KwnD1ZwJGfS//up5J3afZw5SF/D3ADdlI5/3VnwyNOajS1Rkc+d3sBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:11:07.587543Z"},"content_sha256":"2a336feac5a3ca9973075ffb62886750a10e79103b6cfc4676b3b2545913a7ed","schema_version":"1.0","event_id":"sha256:2a336feac5a3ca9973075ffb62886750a10e79103b6cfc4676b3b2545913a7ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GB4BDAAJZ3BUJNR64PVFHXE7PL/bundle.json","state_url":"https://pith.science/pith/GB4BDAAJZ3BUJNR64PVFHXE7PL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GB4BDAAJZ3BUJNR64PVFHXE7PL/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":"2026-05-28T15:11:07Z","links":{"resolver":"https://pith.science/pith/GB4BDAAJZ3BUJNR64PVFHXE7PL","bundle":"https://pith.science/pith/GB4BDAAJZ3BUJNR64PVFHXE7PL/bundle.json","state":"https://pith.science/pith/GB4BDAAJZ3BUJNR64PVFHXE7PL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GB4BDAAJZ3BUJNR64PVFHXE7PL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GB4BDAAJZ3BUJNR64PVFHXE7PL","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":"863c145eb49b9a25415fc61da69e9b275bd0f091a83f301ebd7d58ed9ec0949d","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2018-03-16T08:00:46Z","title_canon_sha256":"6f7a5cae022ff18abb93e4a42d9853a9f8e2cd12d259f8079a09283e96474bf0"},"schema_version":"1.0","source":{"id":"1803.06106","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.06106","created_at":"2026-05-18T00:02:12Z"},{"alias_kind":"arxiv_version","alias_value":"1803.06106v2","created_at":"2026-05-18T00:02:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.06106","created_at":"2026-05-18T00:02:12Z"},{"alias_kind":"pith_short_12","alias_value":"GB4BDAAJZ3BU","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GB4BDAAJZ3BUJNR6","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GB4BDAAJ","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:2a336feac5a3ca9973075ffb62886750a10e79103b6cfc4676b3b2545913a7ed","target":"graph","created_at":"2026-05-18T00:02:12Z","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":"Representation theorems for both isotropic and anisotropic functions are of prime importance in both theoretical and applied mechanics. The Eshelby inclusion problem is very fundamental, and is of particular importance in the design of advanced functional composite materials. In this paper, we discuss about two-dimensional Eshelby tensors (denoted as $M^{(2)}$). Eshelby tensors satisfy the minor index symmetry $M_{ijkl}^{(2)}=M_{jikl}^{(2)}=M_{ijlk}^{(2)}$ and have wide applications in many fields of mechanics. In view of the representation of two-dimensional irreducible tensors in complex fie","authors_text":"Liping Zhang, Yannan Chen, Zhenyu Ming","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2018-03-16T08:00:46Z","title":"An Irreducible Polynomial Functional Basis of Two-dimensional Eshelby Tensors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06106","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":"sha256:2fe637527b0dd1f9ca178f2c037c4908e4197d3596f625aeb7769ce36abd1bd6","target":"record","created_at":"2026-05-18T00:02:12Z","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":"863c145eb49b9a25415fc61da69e9b275bd0f091a83f301ebd7d58ed9ec0949d","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2018-03-16T08:00:46Z","title_canon_sha256":"6f7a5cae022ff18abb93e4a42d9853a9f8e2cd12d259f8079a09283e96474bf0"},"schema_version":"1.0","source":{"id":"1803.06106","kind":"arxiv","version":2}},"canonical_sha256":"3078118009cec344b63ee3ea53dc9f7ad8d5c34a0d2f5aba63b33f8cf13135ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3078118009cec344b63ee3ea53dc9f7ad8d5c34a0d2f5aba63b33f8cf13135ab","first_computed_at":"2026-05-18T00:02:12.663292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:12.663292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IeH1gsD13IuF0qkUCvXkvnb56tBX8r31Utw+w1mOH4RnyybCA12ajyaAr+KEOAkyl1fa4dAOF/V2ZFraTs6UDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:12.664040Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.06106","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fe637527b0dd1f9ca178f2c037c4908e4197d3596f625aeb7769ce36abd1bd6","sha256:2a336feac5a3ca9973075ffb62886750a10e79103b6cfc4676b3b2545913a7ed"],"state_sha256":"5f9a2fd4b7cad60dae8036ccaa22ebe8134cebd9a93a7517491c8c171dcc07ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/N9QdyHGOHQAJenzxXuUruKgvCfZ+t0rE+LQi/c1mDBqq3fM4o08N/awtAwIVLFJnbERJmaKJq520V6qtG+CDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T15:11:07.590904Z","bundle_sha256":"c97e649123c2efd3049535ca9be58758ee281654537f54253a06aa8d2708e797"}}