{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:Z4YVT67UCYNPD7JPKJJI3M72FE","short_pith_number":"pith:Z4YVT67U","canonical_record":{"source":{"id":"2212.09551","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2022-12-19T15:43:31Z","cross_cats_sorted":["math.AG","math.OC"],"title_canon_sha256":"7ea24d6b2fcbb6564c066e84582efc37394f0fe02386c4dda8d32608238af429","abstract_canon_sha256":"0180d10ac3fd5c197186f94aa3920df3af823f1d7d3656c7e77b6d26c00a9f91"},"schema_version":"1.0"},"canonical_sha256":"cf3159fbf4161af1fd2f52528db3fa29140b26dfbecde37bfe204a1250e89b2f","source":{"kind":"arxiv","id":"2212.09551","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.09551","created_at":"2026-07-05T09:05:08Z"},{"alias_kind":"arxiv_version","alias_value":"2212.09551v2","created_at":"2026-07-05T09:05:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.09551","created_at":"2026-07-05T09:05:08Z"},{"alias_kind":"pith_short_12","alias_value":"Z4YVT67UCYNP","created_at":"2026-07-05T09:05:08Z"},{"alias_kind":"pith_short_16","alias_value":"Z4YVT67UCYNPD7JP","created_at":"2026-07-05T09:05:08Z"},{"alias_kind":"pith_short_8","alias_value":"Z4YVT67U","created_at":"2026-07-05T09:05:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:Z4YVT67UCYNPD7JPKJJI3M72FE","target":"record","payload":{"canonical_record":{"source":{"id":"2212.09551","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2022-12-19T15:43:31Z","cross_cats_sorted":["math.AG","math.OC"],"title_canon_sha256":"7ea24d6b2fcbb6564c066e84582efc37394f0fe02386c4dda8d32608238af429","abstract_canon_sha256":"0180d10ac3fd5c197186f94aa3920df3af823f1d7d3656c7e77b6d26c00a9f91"},"schema_version":"1.0"},"canonical_sha256":"cf3159fbf4161af1fd2f52528db3fa29140b26dfbecde37bfe204a1250e89b2f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:05:08.724526Z","signature_b64":"MtCLmKi1QG0Pf5rZTPcOsPvpDt1Yi/caiWxVuYhy23MD6V3XuqBb3+5CN5RDrZMUFUfVfS0M/lbwBSqs7OtUBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf3159fbf4161af1fd2f52528db3fa29140b26dfbecde37bfe204a1250e89b2f","last_reissued_at":"2026-07-05T09:05:08.724079Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:05:08.724079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2212.09551","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":"2026-07-05T09:05:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Aji0BwezcKNN1yHJANm1/zZzuAb6yXiJPQ9NvdwVnvHTR7xR9uogXQ0KDXjKHXqwehTqDbyoTXR2wjO+FsnvDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T10:22:50.782816Z"},"content_sha256":"8673180379866dde6ee628773c68b354d96c2cda5b40349e28def9bb3b7041de","schema_version":"1.0","event_id":"sha256:8673180379866dde6ee628773c68b354d96c2cda5b40349e28def9bb3b7041de"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:Z4YVT67UCYNPD7JPKJJI3M72FE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On {\\L}ojasiewicz Inequalities and the Effective Putinar's Positivstellensatz","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.OC"],"primary_cat":"math.AC","authors_text":"Adam Parusinski (LJAD), Bernard Mourrain (AROMATH), Lorenzo Baldi (AROMATH, PolSys)","submitted_at":"2022-12-19T15:43:31Z","abstract_excerpt":"The representation of positive polynomials on a semi-algebraic set in terms of sums of squares is a central question in real algebraic geometry, which the Positivstellensatz answers. In this paper, we study the effective Putinar's Positivestellensatz on a compact basic semi-algebraic set $S$ and provide a new proof and new improved bounds on the degree of the representation of positive polynomials. These new bounds involve a parameter $\\epsilon$ measuring the non-vanishing of the positive function, the constant $\\mathfrak{c}$ and exponent $L$ of a {\\L}ojasiewicz inequality for the semi-algebra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.09551","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/2212.09551/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":"2026-07-05T09:05:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dOntEYr/lNaJgQdy20Eq5h9xZ3VzjzPDVrm9qvkgz7QTFRYZIZ4EON0rVATi1iX++EgngpsFSJJKK2tEfx52AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T10:22:50.783291Z"},"content_sha256":"0cb440a1ab8e9b9fbae871660f4e77d1b3fc64c54c848e5c30344d0f5bd9d113","schema_version":"1.0","event_id":"sha256:0cb440a1ab8e9b9fbae871660f4e77d1b3fc64c54c848e5c30344d0f5bd9d113"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z4YVT67UCYNPD7JPKJJI3M72FE/bundle.json","state_url":"https://pith.science/pith/Z4YVT67UCYNPD7JPKJJI3M72FE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z4YVT67UCYNPD7JPKJJI3M72FE/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":"2026-08-11T10:22:50Z","links":{"resolver":"https://pith.science/pith/Z4YVT67UCYNPD7JPKJJI3M72FE","bundle":"https://pith.science/pith/Z4YVT67UCYNPD7JPKJJI3M72FE/bundle.json","state":"https://pith.science/pith/Z4YVT67UCYNPD7JPKJJI3M72FE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z4YVT67UCYNPD7JPKJJI3M72FE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:Z4YVT67UCYNPD7JPKJJI3M72FE","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":"0180d10ac3fd5c197186f94aa3920df3af823f1d7d3656c7e77b6d26c00a9f91","cross_cats_sorted":["math.AG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2022-12-19T15:43:31Z","title_canon_sha256":"7ea24d6b2fcbb6564c066e84582efc37394f0fe02386c4dda8d32608238af429"},"schema_version":"1.0","source":{"id":"2212.09551","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.09551","created_at":"2026-07-05T09:05:08Z"},{"alias_kind":"arxiv_version","alias_value":"2212.09551v2","created_at":"2026-07-05T09:05:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.09551","created_at":"2026-07-05T09:05:08Z"},{"alias_kind":"pith_short_12","alias_value":"Z4YVT67UCYNP","created_at":"2026-07-05T09:05:08Z"},{"alias_kind":"pith_short_16","alias_value":"Z4YVT67UCYNPD7JP","created_at":"2026-07-05T09:05:08Z"},{"alias_kind":"pith_short_8","alias_value":"Z4YVT67U","created_at":"2026-07-05T09:05:08Z"}],"graph_snapshots":[{"event_id":"sha256:0cb440a1ab8e9b9fbae871660f4e77d1b3fc64c54c848e5c30344d0f5bd9d113","target":"graph","created_at":"2026-07-05T09:05:08Z","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/2212.09551/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The representation of positive polynomials on a semi-algebraic set in terms of sums of squares is a central question in real algebraic geometry, which the Positivstellensatz answers. In this paper, we study the effective Putinar's Positivestellensatz on a compact basic semi-algebraic set $S$ and provide a new proof and new improved bounds on the degree of the representation of positive polynomials. These new bounds involve a parameter $\\epsilon$ measuring the non-vanishing of the positive function, the constant $\\mathfrak{c}$ and exponent $L$ of a {\\L}ojasiewicz inequality for the semi-algebra","authors_text":"Adam Parusinski (LJAD), Bernard Mourrain (AROMATH), Lorenzo Baldi (AROMATH, PolSys)","cross_cats":["math.AG","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2022-12-19T15:43:31Z","title":"On {\\L}ojasiewicz Inequalities and the Effective Putinar's Positivstellensatz"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.09551","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":"sha256:8673180379866dde6ee628773c68b354d96c2cda5b40349e28def9bb3b7041de","target":"record","created_at":"2026-07-05T09:05:08Z","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":"0180d10ac3fd5c197186f94aa3920df3af823f1d7d3656c7e77b6d26c00a9f91","cross_cats_sorted":["math.AG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2022-12-19T15:43:31Z","title_canon_sha256":"7ea24d6b2fcbb6564c066e84582efc37394f0fe02386c4dda8d32608238af429"},"schema_version":"1.0","source":{"id":"2212.09551","kind":"arxiv","version":2}},"canonical_sha256":"cf3159fbf4161af1fd2f52528db3fa29140b26dfbecde37bfe204a1250e89b2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf3159fbf4161af1fd2f52528db3fa29140b26dfbecde37bfe204a1250e89b2f","first_computed_at":"2026-07-05T09:05:08.724079Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:05:08.724079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MtCLmKi1QG0Pf5rZTPcOsPvpDt1Yi/caiWxVuYhy23MD6V3XuqBb3+5CN5RDrZMUFUfVfS0M/lbwBSqs7OtUBg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:05:08.724526Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.09551","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8673180379866dde6ee628773c68b354d96c2cda5b40349e28def9bb3b7041de","sha256:0cb440a1ab8e9b9fbae871660f4e77d1b3fc64c54c848e5c30344d0f5bd9d113"],"state_sha256":"f81838950549030c2cb34b51c8ba2f647066ed3d4ec27fdcba71b2bd058982cb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jyee78d2Z33ti5c7GjTj7fUPBt12GYMoOoA1h/I9XBDhSrzsulND7vovz239Nn1tPEGINmY+hw4IiDS6kaPgCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T10:22:50.787347Z","bundle_sha256":"20dcd177f5bcfa4dcd5b3a872fe8bc8240811ba3e6475550174b1a8a8e23af43"}}