{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:3RFNKY3H4MOLP5SQNNAX3I2W7X","short_pith_number":"pith:3RFNKY3H","canonical_record":{"source":{"id":"1312.6582","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-23T15:50:09Z","cross_cats_sorted":["cs.CC","math.AT"],"title_canon_sha256":"c413eff0310338b9551eef691291d3b4619fd385adb5623bbd908cede4fde10e","abstract_canon_sha256":"50558eac33e94e486b4dddbdadd240cddb1d53a3dd31c61e442c989472794289"},"schema_version":"1.0"},"canonical_sha256":"dc4ad56367e31cb7f6506b417da356fdedaef74e9e6146ad5c477b1c1ad2554e","source":{"kind":"arxiv","id":"1312.6582","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6582","created_at":"2026-05-18T01:03:10Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6582v6","created_at":"2026-05-18T01:03:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6582","created_at":"2026-05-18T01:03:10Z"},{"alias_kind":"pith_short_12","alias_value":"3RFNKY3H4MOL","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3RFNKY3H4MOLP5SQ","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3RFNKY3H","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:3RFNKY3H4MOLP5SQNNAX3I2W7X","target":"record","payload":{"canonical_record":{"source":{"id":"1312.6582","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-23T15:50:09Z","cross_cats_sorted":["cs.CC","math.AT"],"title_canon_sha256":"c413eff0310338b9551eef691291d3b4619fd385adb5623bbd908cede4fde10e","abstract_canon_sha256":"50558eac33e94e486b4dddbdadd240cddb1d53a3dd31c61e442c989472794289"},"schema_version":"1.0"},"canonical_sha256":"dc4ad56367e31cb7f6506b417da356fdedaef74e9e6146ad5c477b1c1ad2554e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:10.858447Z","signature_b64":"1AWzQLrIgpr+5Qk3sybujZSPQaoEWLikJarl+ZbJLNkAQ4QfZLlw6+5LV4qoCjzBVLz8mFKZdjYd2NIaXDKBBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc4ad56367e31cb7f6506b417da356fdedaef74e9e6146ad5c477b1c1ad2554e","last_reissued_at":"2026-05-18T01:03:10.857763Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:10.857763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.6582","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:03:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LtuzDYHb6g7PiMnqcyUDtDnf/0CJ61O5wnxlHSo4U01/A/sAeikVUpL041RLH8OxMVEQaKY+mXsN38HUuNXEBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:29:34.555137Z"},"content_sha256":"64567dfd4f3c6852c3a1d879d21963e9c07d8068855c7bad5d7523c3ab3f5294","schema_version":"1.0","event_id":"sha256:64567dfd4f3c6852c3a1d879d21963e9c07d8068855c7bad5d7523c3ab3f5294"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:3RFNKY3H4MOLP5SQNNAX3I2W7X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounding the equivariant Betti numbers of symmetric semi-algebraic sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.AT"],"primary_cat":"math.AG","authors_text":"Cordian Riener, Saugata Basu","submitted_at":"2013-12-23T15:50:09Z","abstract_excerpt":"Let $\\mathrm{R}$ be a real closed field. The problem of obtaining tight bounds on the Betti numbers of semi-algebraic subsets of $\\mathrm{R}^k$ in terms of the number and degrees of the defining polynomials has been an important problem in real algebraic geometry with the first results due to Ole{\\u\\i}nik and Petrovski{\\u\\i}, Thom and Milnor. These bounds are all exponential in the number of variables $k$. Motivated by several applications in real algebraic geometry, as well as in theoretical computer science, where such bounds have found applications, we consider in this paper the problem of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6582","kind":"arxiv","version":6},"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":"2026-05-18T01:03:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zuyzYAO9nnmXkKMvs+6wDNPf3clKRwagIoFnuLtO4JNs2VEmGKVI/HTc2Wg72zR00BQ4YVGWO4B24WGr09v+Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:29:34.555710Z"},"content_sha256":"aac130ef65d89fd923bd944000a1f6ae475718190c0af860d20aaee969c2d44b","schema_version":"1.0","event_id":"sha256:aac130ef65d89fd923bd944000a1f6ae475718190c0af860d20aaee969c2d44b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3RFNKY3H4MOLP5SQNNAX3I2W7X/bundle.json","state_url":"https://pith.science/pith/3RFNKY3H4MOLP5SQNNAX3I2W7X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3RFNKY3H4MOLP5SQNNAX3I2W7X/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":"2026-05-28T15:29:34Z","links":{"resolver":"https://pith.science/pith/3RFNKY3H4MOLP5SQNNAX3I2W7X","bundle":"https://pith.science/pith/3RFNKY3H4MOLP5SQNNAX3I2W7X/bundle.json","state":"https://pith.science/pith/3RFNKY3H4MOLP5SQNNAX3I2W7X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3RFNKY3H4MOLP5SQNNAX3I2W7X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3RFNKY3H4MOLP5SQNNAX3I2W7X","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":"50558eac33e94e486b4dddbdadd240cddb1d53a3dd31c61e442c989472794289","cross_cats_sorted":["cs.CC","math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-23T15:50:09Z","title_canon_sha256":"c413eff0310338b9551eef691291d3b4619fd385adb5623bbd908cede4fde10e"},"schema_version":"1.0","source":{"id":"1312.6582","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6582","created_at":"2026-05-18T01:03:10Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6582v6","created_at":"2026-05-18T01:03:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6582","created_at":"2026-05-18T01:03:10Z"},{"alias_kind":"pith_short_12","alias_value":"3RFNKY3H4MOL","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3RFNKY3H4MOLP5SQ","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3RFNKY3H","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:aac130ef65d89fd923bd944000a1f6ae475718190c0af860d20aaee969c2d44b","target":"graph","created_at":"2026-05-18T01:03:10Z","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"},"paper":{"abstract_excerpt":"Let $\\mathrm{R}$ be a real closed field. The problem of obtaining tight bounds on the Betti numbers of semi-algebraic subsets of $\\mathrm{R}^k$ in terms of the number and degrees of the defining polynomials has been an important problem in real algebraic geometry with the first results due to Ole{\\u\\i}nik and Petrovski{\\u\\i}, Thom and Milnor. These bounds are all exponential in the number of variables $k$. Motivated by several applications in real algebraic geometry, as well as in theoretical computer science, where such bounds have found applications, we consider in this paper the problem of ","authors_text":"Cordian Riener, Saugata Basu","cross_cats":["cs.CC","math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-23T15:50:09Z","title":"Bounding the equivariant Betti numbers of symmetric semi-algebraic sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6582","kind":"arxiv","version":6},"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":"sha256:64567dfd4f3c6852c3a1d879d21963e9c07d8068855c7bad5d7523c3ab3f5294","target":"record","created_at":"2026-05-18T01:03:10Z","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":"50558eac33e94e486b4dddbdadd240cddb1d53a3dd31c61e442c989472794289","cross_cats_sorted":["cs.CC","math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-23T15:50:09Z","title_canon_sha256":"c413eff0310338b9551eef691291d3b4619fd385adb5623bbd908cede4fde10e"},"schema_version":"1.0","source":{"id":"1312.6582","kind":"arxiv","version":6}},"canonical_sha256":"dc4ad56367e31cb7f6506b417da356fdedaef74e9e6146ad5c477b1c1ad2554e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc4ad56367e31cb7f6506b417da356fdedaef74e9e6146ad5c477b1c1ad2554e","first_computed_at":"2026-05-18T01:03:10.857763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:10.857763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1AWzQLrIgpr+5Qk3sybujZSPQaoEWLikJarl+ZbJLNkAQ4QfZLlw6+5LV4qoCjzBVLz8mFKZdjYd2NIaXDKBBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:10.858447Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.6582","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64567dfd4f3c6852c3a1d879d21963e9c07d8068855c7bad5d7523c3ab3f5294","sha256:aac130ef65d89fd923bd944000a1f6ae475718190c0af860d20aaee969c2d44b"],"state_sha256":"7a9193b7b05c5775083c49881c42b036c94a277a58b6459cc409506a02f9dd4b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8gcGdp5KmaHHDshP8rdNuob6jq/xSm+ACxI2sGVWAbcxiL1RC5xjrxcPq55cq8XCBwWlx+DtGAIHuK/7nhlhBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T15:29:34.558945Z","bundle_sha256":"fa65bffc0436412839eb8c588773fa81f4734e2b325d9ba56e345f36228a811b"}}