{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:C3S2RPII2LJ66CCNLSEDJXF6WN","short_pith_number":"pith:C3S2RPII","canonical_record":{"source":{"id":"1607.04287","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-07-14T20:00:11Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"c5bcbc088ed8676112138f4d9e9025a91dd529da900bfe0f802d825e4da31fd1","abstract_canon_sha256":"c0a960fae41ed315a45d3645e66fb74a8164e4370236eb4b799d324f3fbb6da1"},"schema_version":"1.0"},"canonical_sha256":"16e5a8bd08d2d3ef084d5c8834dcbeb35f0c3109fd4f9b856c88b7b2b245eb91","source":{"kind":"arxiv","id":"1607.04287","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04287","created_at":"2026-05-18T01:11:01Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04287v1","created_at":"2026-05-18T01:11:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04287","created_at":"2026-05-18T01:11:01Z"},{"alias_kind":"pith_short_12","alias_value":"C3S2RPII2LJ6","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C3S2RPII2LJ66CCN","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C3S2RPII","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:C3S2RPII2LJ66CCNLSEDJXF6WN","target":"record","payload":{"canonical_record":{"source":{"id":"1607.04287","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-07-14T20:00:11Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"c5bcbc088ed8676112138f4d9e9025a91dd529da900bfe0f802d825e4da31fd1","abstract_canon_sha256":"c0a960fae41ed315a45d3645e66fb74a8164e4370236eb4b799d324f3fbb6da1"},"schema_version":"1.0"},"canonical_sha256":"16e5a8bd08d2d3ef084d5c8834dcbeb35f0c3109fd4f9b856c88b7b2b245eb91","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:01.580906Z","signature_b64":"sDzWwoq09HMnvnYZDB4PLDFBVDTfEBdiDDsUakm36WvfDgckxUct0dni2IAfyrJpy6TtYqqVfPEy4lIp0S9lAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16e5a8bd08d2d3ef084d5c8834dcbeb35f0c3109fd4f9b856c88b7b2b245eb91","last_reissued_at":"2026-05-18T01:11:01.580449Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:01.580449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.04287","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":"2026-05-18T01:11:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aF0mptdbk99KwGVGmFczE0ZzvjjpwK5gtOJmY0q77iUzQtyIg2qnTBo9SYTxs2QwNt3u8SB+yCql8SzUu9AJDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T01:25:12.752497Z"},"content_sha256":"16059714d50972c5b3aa5f26b8690f7420155038cf381b6900eae3ba12398dff","schema_version":"1.0","event_id":"sha256:16059714d50972c5b3aa5f26b8690f7420155038cf381b6900eae3ba12398dff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:C3S2RPII2LJ66CCNLSEDJXF6WN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear Diophantine Equations, Group CSPs, and Graph Isomorphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.CC","authors_text":"Christoph Berkholz, Martin Grohe","submitted_at":"2016-07-14T20:00:11Z","abstract_excerpt":"In recent years, we have seen several approaches to the graph isomorphism problem based on \"generic\" mathematical programming or algebraic (Gr\\\"obner basis) techniques. For most of these, lower bounds have been established. In fact, it has been shown that the pairs of nonisomorphic CFI-graphs (introduced by Cai, F\\\"urer, and Immerman in 1992 as hard examples for the combinatorial Weisfeiler-Leman algorithm) cannot be distinguished by these mathematical algorithms. A notable exception were the algebraic algorithms over the field GF(2), for which no lower bound was known. Another, in some way ev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04287","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":"2026-05-18T01:11:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"em0BAIqdBAfHyTlRWQF72QgsYHhLjJVtdn+pRju7UHH/z8RFE2yI1HFMkgPr0CgTxxpM8WYnqxr+nsvuAV42Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T01:25:12.753165Z"},"content_sha256":"d131bd9e46ffec2fff8c9abc486f2d600bd911337d04ca5ed4c5edae1b1c8ebe","schema_version":"1.0","event_id":"sha256:d131bd9e46ffec2fff8c9abc486f2d600bd911337d04ca5ed4c5edae1b1c8ebe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C3S2RPII2LJ66CCNLSEDJXF6WN/bundle.json","state_url":"https://pith.science/pith/C3S2RPII2LJ66CCNLSEDJXF6WN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C3S2RPII2LJ66CCNLSEDJXF6WN/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":"2026-06-06T01:25:12Z","links":{"resolver":"https://pith.science/pith/C3S2RPII2LJ66CCNLSEDJXF6WN","bundle":"https://pith.science/pith/C3S2RPII2LJ66CCNLSEDJXF6WN/bundle.json","state":"https://pith.science/pith/C3S2RPII2LJ66CCNLSEDJXF6WN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C3S2RPII2LJ66CCNLSEDJXF6WN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:C3S2RPII2LJ66CCNLSEDJXF6WN","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":"c0a960fae41ed315a45d3645e66fb74a8164e4370236eb4b799d324f3fbb6da1","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-07-14T20:00:11Z","title_canon_sha256":"c5bcbc088ed8676112138f4d9e9025a91dd529da900bfe0f802d825e4da31fd1"},"schema_version":"1.0","source":{"id":"1607.04287","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04287","created_at":"2026-05-18T01:11:01Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04287v1","created_at":"2026-05-18T01:11:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04287","created_at":"2026-05-18T01:11:01Z"},{"alias_kind":"pith_short_12","alias_value":"C3S2RPII2LJ6","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C3S2RPII2LJ66CCN","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C3S2RPII","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:d131bd9e46ffec2fff8c9abc486f2d600bd911337d04ca5ed4c5edae1b1c8ebe","target":"graph","created_at":"2026-05-18T01:11:01Z","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":"In recent years, we have seen several approaches to the graph isomorphism problem based on \"generic\" mathematical programming or algebraic (Gr\\\"obner basis) techniques. For most of these, lower bounds have been established. In fact, it has been shown that the pairs of nonisomorphic CFI-graphs (introduced by Cai, F\\\"urer, and Immerman in 1992 as hard examples for the combinatorial Weisfeiler-Leman algorithm) cannot be distinguished by these mathematical algorithms. A notable exception were the algebraic algorithms over the field GF(2), for which no lower bound was known. Another, in some way ev","authors_text":"Christoph Berkholz, Martin Grohe","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-07-14T20:00:11Z","title":"Linear Diophantine Equations, Group CSPs, and Graph Isomorphism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04287","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":"sha256:16059714d50972c5b3aa5f26b8690f7420155038cf381b6900eae3ba12398dff","target":"record","created_at":"2026-05-18T01:11:01Z","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":"c0a960fae41ed315a45d3645e66fb74a8164e4370236eb4b799d324f3fbb6da1","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-07-14T20:00:11Z","title_canon_sha256":"c5bcbc088ed8676112138f4d9e9025a91dd529da900bfe0f802d825e4da31fd1"},"schema_version":"1.0","source":{"id":"1607.04287","kind":"arxiv","version":1}},"canonical_sha256":"16e5a8bd08d2d3ef084d5c8834dcbeb35f0c3109fd4f9b856c88b7b2b245eb91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16e5a8bd08d2d3ef084d5c8834dcbeb35f0c3109fd4f9b856c88b7b2b245eb91","first_computed_at":"2026-05-18T01:11:01.580449Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:01.580449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sDzWwoq09HMnvnYZDB4PLDFBVDTfEBdiDDsUakm36WvfDgckxUct0dni2IAfyrJpy6TtYqqVfPEy4lIp0S9lAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:01.580906Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.04287","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16059714d50972c5b3aa5f26b8690f7420155038cf381b6900eae3ba12398dff","sha256:d131bd9e46ffec2fff8c9abc486f2d600bd911337d04ca5ed4c5edae1b1c8ebe"],"state_sha256":"b1ebb6a60e53eacdfcb797d31d4c7f26d5c683aedb5aeb5eeb6da1bb986d79af"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i/sSAtm8Jw+5eod+fCFAAFtjtD7s57k5fWFCzEsIlYL5AM/bBb1szx6rryPeSirZZxJya0NhETeCagPOUicfDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T01:25:12.757047Z","bundle_sha256":"b1308c9cf63babb6034bb366424137346274507ceebb577c457fe0ee26eb29dc"}}