{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ZAANUDNGW4YHD4S5TTBNIZ55PM","short_pith_number":"pith:ZAANUDNG","canonical_record":{"source":{"id":"2608.07087","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-07T10:39:36Z","cross_cats_sorted":[],"title_canon_sha256":"150033b9cbc36fbbd12bb88b9fc673bdb6dcffe115ed973eda970246d61c23c1","abstract_canon_sha256":"8c9ad32718001d8bbe70fadb0cb104aee8f4e45cd2b8dac7dd5fe2b194f5d13d"},"schema_version":"1.0"},"canonical_sha256":"c800da0da6b73071f25d9cc2d467bd7b23d13e2abb82783420ddffe058541d33","source":{"kind":"arxiv","id":"2608.07087","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.07087","created_at":"2026-08-10T01:13:10Z"},{"alias_kind":"arxiv_version","alias_value":"2608.07087v1","created_at":"2026-08-10T01:13:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.07087","created_at":"2026-08-10T01:13:10Z"},{"alias_kind":"pith_short_12","alias_value":"ZAANUDNGW4YH","created_at":"2026-08-10T01:13:10Z"},{"alias_kind":"pith_short_16","alias_value":"ZAANUDNGW4YHD4S5","created_at":"2026-08-10T01:13:10Z"},{"alias_kind":"pith_short_8","alias_value":"ZAANUDNG","created_at":"2026-08-10T01:13:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ZAANUDNGW4YHD4S5TTBNIZ55PM","target":"record","payload":{"canonical_record":{"source":{"id":"2608.07087","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-07T10:39:36Z","cross_cats_sorted":[],"title_canon_sha256":"150033b9cbc36fbbd12bb88b9fc673bdb6dcffe115ed973eda970246d61c23c1","abstract_canon_sha256":"8c9ad32718001d8bbe70fadb0cb104aee8f4e45cd2b8dac7dd5fe2b194f5d13d"},"schema_version":"1.0"},"canonical_sha256":"c800da0da6b73071f25d9cc2d467bd7b23d13e2abb82783420ddffe058541d33","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-10T01:13:10.931399Z","signature_b64":"iYqy3Vs/3wkO2m6YJXyrAbqPehKKaweCJlsOFq6aT/qa/2f8SETgIfpWywlDnln5hN4kOSdvp7s2aDEQsZxOAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c800da0da6b73071f25d9cc2d467bd7b23d13e2abb82783420ddffe058541d33","last_reissued_at":"2026-08-10T01:13:10.928206Z","signature_status":"signed_v1","first_computed_at":"2026-08-10T01:13:10.928206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.07087","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":"2026-08-10T01:13:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+TSM3VvUKyK8MFoA2Jmqv50OS4Ym/grUJ9FE67VItMMQAwARWPzbOGEfV66Wp4pzw7Qe6lvHms9ZCpPfRbogCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T16:54:55.075714Z"},"content_sha256":"2e849563ffc002a7f4e103dc193a9ff0168f888b1779c42a99d343ede2f489bc","schema_version":"1.0","event_id":"sha256:2e849563ffc002a7f4e103dc193a9ff0168f888b1779c42a99d343ede2f489bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ZAANUDNGW4YHD4S5TTBNIZ55PM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ionel-Dumitrel Ghiba, Jendrik Voss, Macro Valerio d'Agostino, Patrizio Neff, Robert J. Martin","submitted_at":"2026-08-07T10:39:36Z","abstract_excerpt":"Motivated by classical constitutive inequalities in isotropic nonlinear elasticity theory, we investigate the monotonicity of isotropic tensor functions of the form\n  \\[\n  \\Sigma_f\\colon\\mathrm{Sym}(n)\\to\\mathrm{Sym}(n)\\,,\\quad \\Sigma_f(Q^T\\mathrm{diag}(\\lambda_1,\\dotsc,\\lambda_n)\\, Q) = Q^T\\mathrm{diag}(f(\\lambda_1,\\dotsc,\\lambda_n))\\, Q \\quad\\forall\\;Q\\in\\mathrm{O}(n)\n  \\]\n  with a vector function $f=(f_1,\\dotsc,f_n)\\colon\\mathbb{R}^n\\to\\mathbb{R}^n$ which is symmetric, i.e.\\ satisfies\n  \\[\n  f_i(\\lambda_{\\pi(1)},\\dotsc,\\lambda_{\\pi(n)}) = f_{\\pi(i)}(\\lambda_1,\\dotsc,\\lambda_n)\n  \\]\n  for an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.07087","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.07087/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-08-10T01:13:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DF9s9iTAB5OH4GJgUKuVIdm+ivRzdelodHm1QvVVGHgyy0hlr/hudXY750ZJgNaQSdlq8UjeiyBQ7jiG2ZCbAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T16:54:55.076172Z"},"content_sha256":"7a093a1ad8044160fa0dc27a3de0f3b7a8079371bdfe39bc1e6c73a7ddc26e1d","schema_version":"1.0","event_id":"sha256:7a093a1ad8044160fa0dc27a3de0f3b7a8079371bdfe39bc1e6c73a7ddc26e1d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZAANUDNGW4YHD4S5TTBNIZ55PM/bundle.json","state_url":"https://pith.science/pith/ZAANUDNGW4YHD4S5TTBNIZ55PM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZAANUDNGW4YHD4S5TTBNIZ55PM/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":"2026-08-17T16:54:55Z","links":{"resolver":"https://pith.science/pith/ZAANUDNGW4YHD4S5TTBNIZ55PM","bundle":"https://pith.science/pith/ZAANUDNGW4YHD4S5TTBNIZ55PM/bundle.json","state":"https://pith.science/pith/ZAANUDNGW4YHD4S5TTBNIZ55PM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZAANUDNGW4YHD4S5TTBNIZ55PM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZAANUDNGW4YHD4S5TTBNIZ55PM","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":"8c9ad32718001d8bbe70fadb0cb104aee8f4e45cd2b8dac7dd5fe2b194f5d13d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-07T10:39:36Z","title_canon_sha256":"150033b9cbc36fbbd12bb88b9fc673bdb6dcffe115ed973eda970246d61c23c1"},"schema_version":"1.0","source":{"id":"2608.07087","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.07087","created_at":"2026-08-10T01:13:10Z"},{"alias_kind":"arxiv_version","alias_value":"2608.07087v1","created_at":"2026-08-10T01:13:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.07087","created_at":"2026-08-10T01:13:10Z"},{"alias_kind":"pith_short_12","alias_value":"ZAANUDNGW4YH","created_at":"2026-08-10T01:13:10Z"},{"alias_kind":"pith_short_16","alias_value":"ZAANUDNGW4YHD4S5","created_at":"2026-08-10T01:13:10Z"},{"alias_kind":"pith_short_8","alias_value":"ZAANUDNG","created_at":"2026-08-10T01:13:10Z"}],"graph_snapshots":[{"event_id":"sha256:7a093a1ad8044160fa0dc27a3de0f3b7a8079371bdfe39bc1e6c73a7ddc26e1d","target":"graph","created_at":"2026-08-10T01:13:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.07087/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Motivated by classical constitutive inequalities in isotropic nonlinear elasticity theory, we investigate the monotonicity of isotropic tensor functions of the form\n  \\[\n  \\Sigma_f\\colon\\mathrm{Sym}(n)\\to\\mathrm{Sym}(n)\\,,\\quad \\Sigma_f(Q^T\\mathrm{diag}(\\lambda_1,\\dotsc,\\lambda_n)\\, Q) = Q^T\\mathrm{diag}(f(\\lambda_1,\\dotsc,\\lambda_n))\\, Q \\quad\\forall\\;Q\\in\\mathrm{O}(n)\n  \\]\n  with a vector function $f=(f_1,\\dotsc,f_n)\\colon\\mathbb{R}^n\\to\\mathbb{R}^n$ which is symmetric, i.e.\\ satisfies\n  \\[\n  f_i(\\lambda_{\\pi(1)},\\dotsc,\\lambda_{\\pi(n)}) = f_{\\pi(i)}(\\lambda_1,\\dotsc,\\lambda_n)\n  \\]\n  for an","authors_text":"Ionel-Dumitrel Ghiba, Jendrik Voss, Macro Valerio d'Agostino, Patrizio Neff, Robert J. Martin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-07T10:39:36Z","title":"Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.07087","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":"sha256:2e849563ffc002a7f4e103dc193a9ff0168f888b1779c42a99d343ede2f489bc","target":"record","created_at":"2026-08-10T01:13:10Z","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":"8c9ad32718001d8bbe70fadb0cb104aee8f4e45cd2b8dac7dd5fe2b194f5d13d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-07T10:39:36Z","title_canon_sha256":"150033b9cbc36fbbd12bb88b9fc673bdb6dcffe115ed973eda970246d61c23c1"},"schema_version":"1.0","source":{"id":"2608.07087","kind":"arxiv","version":1}},"canonical_sha256":"c800da0da6b73071f25d9cc2d467bd7b23d13e2abb82783420ddffe058541d33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c800da0da6b73071f25d9cc2d467bd7b23d13e2abb82783420ddffe058541d33","first_computed_at":"2026-08-10T01:13:10.928206Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-10T01:13:10.928206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iYqy3Vs/3wkO2m6YJXyrAbqPehKKaweCJlsOFq6aT/qa/2f8SETgIfpWywlDnln5hN4kOSdvp7s2aDEQsZxOAg==","signature_status":"signed_v1","signed_at":"2026-08-10T01:13:10.931399Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.07087","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e849563ffc002a7f4e103dc193a9ff0168f888b1779c42a99d343ede2f489bc","sha256:7a093a1ad8044160fa0dc27a3de0f3b7a8079371bdfe39bc1e6c73a7ddc26e1d"],"state_sha256":"011d101adcca71ee397c8a1c4cc5d67f1cc56a5c06a859f93ddfb249d0a06141"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wqho3fFdbBhKJ81JFzHnDN7RfT6o3zuAwieb1yXnulv8KHgvNxwZid93GgCkPX8qkqvWXb6fCJENVyJ24etmDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T16:54:55.098840Z","bundle_sha256":"8fdbbffc4ba0cb10696bf053cf43cdc652a9ed7f1c641d61c1197e950aa59841"}}