{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:BWRIHA6NAMRZEHXBLKOPKLS7OE","short_pith_number":"pith:BWRIHA6N","canonical_record":{"source":{"id":"2206.10913","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-06-22T08:43:09Z","cross_cats_sorted":[],"title_canon_sha256":"829723db37dabdcb7066485db5a95445b7bb5108f866abb1c272d7e4c18b6fc7","abstract_canon_sha256":"2f76523f40146ff374d8d60baf66840b09077698ab9a3c08a3162670e9c7a9a5"},"schema_version":"1.0"},"canonical_sha256":"0da28383cd0323921ee15a9cf52e5f71148a2a146be6606136995d468e340961","source":{"kind":"arxiv","id":"2206.10913","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.10913","created_at":"2026-07-05T05:19:53Z"},{"alias_kind":"arxiv_version","alias_value":"2206.10913v2","created_at":"2026-07-05T05:19:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.10913","created_at":"2026-07-05T05:19:53Z"},{"alias_kind":"pith_short_12","alias_value":"BWRIHA6NAMRZ","created_at":"2026-07-05T05:19:53Z"},{"alias_kind":"pith_short_16","alias_value":"BWRIHA6NAMRZEHXB","created_at":"2026-07-05T05:19:53Z"},{"alias_kind":"pith_short_8","alias_value":"BWRIHA6N","created_at":"2026-07-05T05:19:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:BWRIHA6NAMRZEHXBLKOPKLS7OE","target":"record","payload":{"canonical_record":{"source":{"id":"2206.10913","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-06-22T08:43:09Z","cross_cats_sorted":[],"title_canon_sha256":"829723db37dabdcb7066485db5a95445b7bb5108f866abb1c272d7e4c18b6fc7","abstract_canon_sha256":"2f76523f40146ff374d8d60baf66840b09077698ab9a3c08a3162670e9c7a9a5"},"schema_version":"1.0"},"canonical_sha256":"0da28383cd0323921ee15a9cf52e5f71148a2a146be6606136995d468e340961","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:19:53.789858Z","signature_b64":"IoW0C4/QL4rjUagpF20JU/MgQWFQAUPtSRCeirAZXPbKMhxpsgLU/OGWpAIAH8sXzBe/y9Qs88FMZ8Kl+YP0BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0da28383cd0323921ee15a9cf52e5f71148a2a146be6606136995d468e340961","last_reissued_at":"2026-07-05T05:19:53.789430Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:19:53.789430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2206.10913","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":"2026-07-05T05:19:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7edMTBcsqTcgYP4bEa3qWdEWGsc8xM5ukkygmnDXaJftuec/x9b15mFSVdqKnYn73L8STnp4rOK1t4Kc5zxmAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T19:53:29.959000Z"},"content_sha256":"3fe4181aff6a693e0efa3a5c171bd949fb2c20db5f716b1ac381c83435df38c6","schema_version":"1.0","event_id":"sha256:3fe4181aff6a693e0efa3a5c171bd949fb2c20db5f716b1ac381c83435df38c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:BWRIHA6NAMRZEHXBLKOPKLS7OE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Combinatorics and preservation of conically stable polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Giulia Codenotti, Stephan Gardoll, Thorsten Theobald","submitted_at":"2022-06-22T08:43:09Z","abstract_excerpt":"Given a closed, convex cone $K\\subseteq \\mathbb{R}^n$, a multivariate polynomial $f\\in\\mathbb{C}[\\mathbf{z}]$ is called $K$-stable if the imaginary parts of its roots are not contained in the relative interior of $K$. If $K$ is the non-negative orthant, $K$-stability specializes to the usual notion of stability of polynomials.\n  We develop generalizations of preservation operations and of combinatorial criteria from usual stability towards conic stability. A particular focus is on the cone of positive semidefinite matrices (psd-stability). In particular, we prove the preservation of psd-stabil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.10913","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2206.10913/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":"2026-07-05T05:19:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ST/vNq4Um1PS1yW19LD0G8CONqVlyJ1MvAa5188NUmsts6wH+xWkLo8maqgZuAZ07vj3FPcyfE1vCyW8RKirCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T19:53:29.959914Z"},"content_sha256":"65423a6c365cef5a811200e9aeb31653548a44aaf3d3c8e6ce7fa634b84968e6","schema_version":"1.0","event_id":"sha256:65423a6c365cef5a811200e9aeb31653548a44aaf3d3c8e6ce7fa634b84968e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BWRIHA6NAMRZEHXBLKOPKLS7OE/bundle.json","state_url":"https://pith.science/pith/BWRIHA6NAMRZEHXBLKOPKLS7OE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BWRIHA6NAMRZEHXBLKOPKLS7OE/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":"2026-08-03T19:53:29Z","links":{"resolver":"https://pith.science/pith/BWRIHA6NAMRZEHXBLKOPKLS7OE","bundle":"https://pith.science/pith/BWRIHA6NAMRZEHXBLKOPKLS7OE/bundle.json","state":"https://pith.science/pith/BWRIHA6NAMRZEHXBLKOPKLS7OE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BWRIHA6NAMRZEHXBLKOPKLS7OE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:BWRIHA6NAMRZEHXBLKOPKLS7OE","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":"2f76523f40146ff374d8d60baf66840b09077698ab9a3c08a3162670e9c7a9a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-06-22T08:43:09Z","title_canon_sha256":"829723db37dabdcb7066485db5a95445b7bb5108f866abb1c272d7e4c18b6fc7"},"schema_version":"1.0","source":{"id":"2206.10913","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.10913","created_at":"2026-07-05T05:19:53Z"},{"alias_kind":"arxiv_version","alias_value":"2206.10913v2","created_at":"2026-07-05T05:19:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.10913","created_at":"2026-07-05T05:19:53Z"},{"alias_kind":"pith_short_12","alias_value":"BWRIHA6NAMRZ","created_at":"2026-07-05T05:19:53Z"},{"alias_kind":"pith_short_16","alias_value":"BWRIHA6NAMRZEHXB","created_at":"2026-07-05T05:19:53Z"},{"alias_kind":"pith_short_8","alias_value":"BWRIHA6N","created_at":"2026-07-05T05:19:53Z"}],"graph_snapshots":[{"event_id":"sha256:65423a6c365cef5a811200e9aeb31653548a44aaf3d3c8e6ce7fa634b84968e6","target":"graph","created_at":"2026-07-05T05:19:53Z","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/2206.10913/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a closed, convex cone $K\\subseteq \\mathbb{R}^n$, a multivariate polynomial $f\\in\\mathbb{C}[\\mathbf{z}]$ is called $K$-stable if the imaginary parts of its roots are not contained in the relative interior of $K$. If $K$ is the non-negative orthant, $K$-stability specializes to the usual notion of stability of polynomials.\n  We develop generalizations of preservation operations and of combinatorial criteria from usual stability towards conic stability. A particular focus is on the cone of positive semidefinite matrices (psd-stability). In particular, we prove the preservation of psd-stabil","authors_text":"Giulia Codenotti, Stephan Gardoll, Thorsten Theobald","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-06-22T08:43:09Z","title":"Combinatorics and preservation of conically stable polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.10913","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":"sha256:3fe4181aff6a693e0efa3a5c171bd949fb2c20db5f716b1ac381c83435df38c6","target":"record","created_at":"2026-07-05T05:19:53Z","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":"2f76523f40146ff374d8d60baf66840b09077698ab9a3c08a3162670e9c7a9a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-06-22T08:43:09Z","title_canon_sha256":"829723db37dabdcb7066485db5a95445b7bb5108f866abb1c272d7e4c18b6fc7"},"schema_version":"1.0","source":{"id":"2206.10913","kind":"arxiv","version":2}},"canonical_sha256":"0da28383cd0323921ee15a9cf52e5f71148a2a146be6606136995d468e340961","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0da28383cd0323921ee15a9cf52e5f71148a2a146be6606136995d468e340961","first_computed_at":"2026-07-05T05:19:53.789430Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:19:53.789430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IoW0C4/QL4rjUagpF20JU/MgQWFQAUPtSRCeirAZXPbKMhxpsgLU/OGWpAIAH8sXzBe/y9Qs88FMZ8Kl+YP0BA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:19:53.789858Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.10913","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3fe4181aff6a693e0efa3a5c171bd949fb2c20db5f716b1ac381c83435df38c6","sha256:65423a6c365cef5a811200e9aeb31653548a44aaf3d3c8e6ce7fa634b84968e6"],"state_sha256":"c500c9d4c1318ef93d8a7d840d6a7fd0ec35952453dc8d4b0c49d21d4de9cd2a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UpCfMPGX/26fHQ1h7QOo9hAR4Ks3OplD0qmhHJNbNuqL7Xu0+VbWEEu0D3xmNPfHBol9VF8C9HKRsjPCgrOKCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T19:53:29.965655Z","bundle_sha256":"01d48b597a695ed25222f4742f012047e73adbfc69bc9221eb251c50062b6c39"}}