{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:FP4UV2YNFUPU5LQKR5P2OPYAIH","short_pith_number":"pith:FP4UV2YN","canonical_record":{"source":{"id":"1206.6318","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-06-27T16:01:42Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"f677fc6941b8d20ea5a98535c8c8c9ce2e64f12c94fd955136a6f5bdd42cabe9","abstract_canon_sha256":"2177843ffb727fc9add54cb8b17d52b4ea09523cbd92dc051bc47d5467c5ccc8"},"schema_version":"1.0"},"canonical_sha256":"2bf94aeb0d2d1f4eae0a8f5fa73f0041e13b4388111e6c3820d367654aa710b5","source":{"kind":"arxiv","id":"1206.6318","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.6318","created_at":"2026-05-18T03:52:26Z"},{"alias_kind":"arxiv_version","alias_value":"1206.6318v1","created_at":"2026-05-18T03:52:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.6318","created_at":"2026-05-18T03:52:26Z"},{"alias_kind":"pith_short_12","alias_value":"FP4UV2YNFUPU","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FP4UV2YNFUPU5LQK","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FP4UV2YN","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:FP4UV2YNFUPU5LQKR5P2OPYAIH","target":"record","payload":{"canonical_record":{"source":{"id":"1206.6318","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-06-27T16:01:42Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"f677fc6941b8d20ea5a98535c8c8c9ce2e64f12c94fd955136a6f5bdd42cabe9","abstract_canon_sha256":"2177843ffb727fc9add54cb8b17d52b4ea09523cbd92dc051bc47d5467c5ccc8"},"schema_version":"1.0"},"canonical_sha256":"2bf94aeb0d2d1f4eae0a8f5fa73f0041e13b4388111e6c3820d367654aa710b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:26.990136Z","signature_b64":"GvTeRscuVf3yIfz/Lt4SyumVL2/uHplHvwuaDjWwugcOLJJC2UuNhe8pIsV2+bZ+wd1DBwSmwdEPR2q7Bx0NAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2bf94aeb0d2d1f4eae0a8f5fa73f0041e13b4388111e6c3820d367654aa710b5","last_reissued_at":"2026-05-18T03:52:26.989477Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:26.989477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.6318","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":"2026-05-18T03:52:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uPkwmsEUIbywNOYzYmSgEWEbalLuXHWj32GOWjP+/RdJGab3B75L/EpxaHlN5X6vsoOWoewglNZRvhNT7t4CAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T00:13:54.083934Z"},"content_sha256":"1d09f31f84ad6408321dd54b0d551df8c0d6134d606856e155374c0c7eb6d7c5","schema_version":"1.0","event_id":"sha256:1d09f31f84ad6408321dd54b0d551df8c0d6134d606856e155374c0c7eb6d7c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:FP4UV2YNFUPU5LQKR5P2OPYAIH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An algebraic approach to symmetric extended formulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CC","authors_text":"G\\'abor Braun, Sebastian Pokutta","submitted_at":"2012-06-27T16:01:42Z","abstract_excerpt":"Extended formulations are an important tool to obtain small (even compact) formulations of polytopes by representing them as projections of higher dimensional ones. It is an important question whether a polytope admits a small extended formulation, i.e., one involving only a polynomial number of inequalities in its dimension. For the case of symmetric extended formulations (i.e., preserving the symmetries of the polytope) Yannakakis established a powerful technique to derive lower bounds and rule out small formulations. We rephrase the technique of Yannakakis in a group-theoretic framework. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6318","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":""},"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":"2026-05-18T03:52:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6j7uOKaX9nDhm7EhgqX4cOL6L0140gQL74WUpAcm6eh0KS6r/g51sgxFRYNoyB/3CYF0+Oulk6eSAfuNhYvACw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T00:13:54.084630Z"},"content_sha256":"c600683deefff196943f42cd55d422fb88bcdf0a5a23a1fe830e1e24bcbd89d1","schema_version":"1.0","event_id":"sha256:c600683deefff196943f42cd55d422fb88bcdf0a5a23a1fe830e1e24bcbd89d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FP4UV2YNFUPU5LQKR5P2OPYAIH/bundle.json","state_url":"https://pith.science/pith/FP4UV2YNFUPU5LQKR5P2OPYAIH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FP4UV2YNFUPU5LQKR5P2OPYAIH/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":"2026-05-24T00:13:54Z","links":{"resolver":"https://pith.science/pith/FP4UV2YNFUPU5LQKR5P2OPYAIH","bundle":"https://pith.science/pith/FP4UV2YNFUPU5LQKR5P2OPYAIH/bundle.json","state":"https://pith.science/pith/FP4UV2YNFUPU5LQKR5P2OPYAIH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FP4UV2YNFUPU5LQKR5P2OPYAIH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FP4UV2YNFUPU5LQKR5P2OPYAIH","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":"2177843ffb727fc9add54cb8b17d52b4ea09523cbd92dc051bc47d5467c5ccc8","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-06-27T16:01:42Z","title_canon_sha256":"f677fc6941b8d20ea5a98535c8c8c9ce2e64f12c94fd955136a6f5bdd42cabe9"},"schema_version":"1.0","source":{"id":"1206.6318","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.6318","created_at":"2026-05-18T03:52:26Z"},{"alias_kind":"arxiv_version","alias_value":"1206.6318v1","created_at":"2026-05-18T03:52:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.6318","created_at":"2026-05-18T03:52:26Z"},{"alias_kind":"pith_short_12","alias_value":"FP4UV2YNFUPU","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FP4UV2YNFUPU5LQK","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FP4UV2YN","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:c600683deefff196943f42cd55d422fb88bcdf0a5a23a1fe830e1e24bcbd89d1","target":"graph","created_at":"2026-05-18T03:52:26Z","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":"Extended formulations are an important tool to obtain small (even compact) formulations of polytopes by representing them as projections of higher dimensional ones. It is an important question whether a polytope admits a small extended formulation, i.e., one involving only a polynomial number of inequalities in its dimension. For the case of symmetric extended formulations (i.e., preserving the symmetries of the polytope) Yannakakis established a powerful technique to derive lower bounds and rule out small formulations. We rephrase the technique of Yannakakis in a group-theoretic framework. Th","authors_text":"G\\'abor Braun, Sebastian Pokutta","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-06-27T16:01:42Z","title":"An algebraic approach to symmetric extended formulations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6318","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":"sha256:1d09f31f84ad6408321dd54b0d551df8c0d6134d606856e155374c0c7eb6d7c5","target":"record","created_at":"2026-05-18T03:52:26Z","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":"2177843ffb727fc9add54cb8b17d52b4ea09523cbd92dc051bc47d5467c5ccc8","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-06-27T16:01:42Z","title_canon_sha256":"f677fc6941b8d20ea5a98535c8c8c9ce2e64f12c94fd955136a6f5bdd42cabe9"},"schema_version":"1.0","source":{"id":"1206.6318","kind":"arxiv","version":1}},"canonical_sha256":"2bf94aeb0d2d1f4eae0a8f5fa73f0041e13b4388111e6c3820d367654aa710b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2bf94aeb0d2d1f4eae0a8f5fa73f0041e13b4388111e6c3820d367654aa710b5","first_computed_at":"2026-05-18T03:52:26.989477Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:26.989477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GvTeRscuVf3yIfz/Lt4SyumVL2/uHplHvwuaDjWwugcOLJJC2UuNhe8pIsV2+bZ+wd1DBwSmwdEPR2q7Bx0NAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:26.990136Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.6318","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d09f31f84ad6408321dd54b0d551df8c0d6134d606856e155374c0c7eb6d7c5","sha256:c600683deefff196943f42cd55d422fb88bcdf0a5a23a1fe830e1e24bcbd89d1"],"state_sha256":"da11d2cd49aeec9ff6d3ebbc63a3e9018ac4162cfb6ada272f9bd89498a1a500"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"id4M5Lg6XWJQc8EETSHP4GA9krq3O3YeUVXcpyPIowiNwdjbOob6VV7cwKxagCJmeqbYbYUxpCNBnBAwY+hvCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T00:13:54.087430Z","bundle_sha256":"8c5aafaf6362a44fad977b195648004d5aa2d67456aaeac9d6b44d004a57950d"}}