{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:2FD3IQFPOAVK2UMJ6GMTMDZBDU","short_pith_number":"pith:2FD3IQFP","canonical_record":{"source":{"id":"1710.00374","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-01T16:19:24Z","cross_cats_sorted":[],"title_canon_sha256":"f76635c283ded8931680917246d0da6e4ff5fe83d3bd697068df8712c78e964b","abstract_canon_sha256":"b121e3807936a403f9dc5c3f32ca209770012d2b5dc4254eea570612879790ae"},"schema_version":"1.0"},"canonical_sha256":"d147b440af702aad5189f199360f211d2884a26f17b36dc5fd6a7a345ff75fa8","source":{"kind":"arxiv","id":"1710.00374","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00374","created_at":"2026-05-18T00:33:54Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00374v1","created_at":"2026-05-18T00:33:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00374","created_at":"2026-05-18T00:33:54Z"},{"alias_kind":"pith_short_12","alias_value":"2FD3IQFPOAVK","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2FD3IQFPOAVK2UMJ","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2FD3IQFP","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:2FD3IQFPOAVK2UMJ6GMTMDZBDU","target":"record","payload":{"canonical_record":{"source":{"id":"1710.00374","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-01T16:19:24Z","cross_cats_sorted":[],"title_canon_sha256":"f76635c283ded8931680917246d0da6e4ff5fe83d3bd697068df8712c78e964b","abstract_canon_sha256":"b121e3807936a403f9dc5c3f32ca209770012d2b5dc4254eea570612879790ae"},"schema_version":"1.0"},"canonical_sha256":"d147b440af702aad5189f199360f211d2884a26f17b36dc5fd6a7a345ff75fa8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:54.977108Z","signature_b64":"3ezHa+bx3/In0OnZV5jpATD/qkR3qZv/pNXWjwOA61DSBw30TMYN0d8mGONqoEE3ZqnnPh2AvdLywDK5EyiRAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d147b440af702aad5189f199360f211d2884a26f17b36dc5fd6a7a345ff75fa8","last_reissued_at":"2026-05-18T00:33:54.976552Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:54.976552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.00374","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":"2026-05-18T00:33:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f2vK8Wcll4t64E/0KdrTTxDP7dIUEUUk8nlZvfurSfKpuDA5EMevD6ZUqXuXbqA73jPDgS7Yl16x+wAus2sWBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:07:56.591464Z"},"content_sha256":"0280352139ee9456168eac3269f679337322dc6853d388e61c0e3d99ae1c5b40","schema_version":"1.0","event_id":"sha256:0280352139ee9456168eac3269f679337322dc6853d388e61c0e3d99ae1c5b40"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:2FD3IQFPOAVK2UMJ6GMTMDZBDU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multivalued matrices and forbidden configurations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Attila Sali, Jeffrey Dawson, Linyuan Lu, Richard Anstee","submitted_at":"2017-10-01T16:19:24Z","abstract_excerpt":"An $r$-matrix is a matrix with symbols in $\\{0,1,\\ldots,r-1\\}$. A matrix is simple if it has no repeated columns. Let ${\\cal F}$ be a finite set of $r$-matrices. Let $\\hbox{forb}(m,r,{\\cal F})$ denote the maximum number of columns possible in a simple $r$-matrix\n  $A$ that has no submatrix which is a row and column permutation of any $F\\in{\\cal F}$. Many investigations have involved $r=2$. For general $r$, $\\hbox{forb}(m,r,{\\cal F})$ is polynomial in $m$ if and only if for every pair $i,j\\in\\{0,1,\\ldots,r-1\\}$ there is a matrix in ${\\cal F}$ whose entries are only $i$ or $j$.\n  Let ${\\cal T}_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00374","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":"2026-05-18T00:33:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"73XvoZA+WvogjTB+0pVRdazREJlUxAvm590RiDcOEEFoBuxCfeV0xOGXjmvL2afWfUg8a30segvQdqvVLMrsCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:07:56.591889Z"},"content_sha256":"ff3df06e99e76f115e8b29b886154f9783d100bc8b2ed1af474d1dc08e1ba935","schema_version":"1.0","event_id":"sha256:ff3df06e99e76f115e8b29b886154f9783d100bc8b2ed1af474d1dc08e1ba935"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2FD3IQFPOAVK2UMJ6GMTMDZBDU/bundle.json","state_url":"https://pith.science/pith/2FD3IQFPOAVK2UMJ6GMTMDZBDU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2FD3IQFPOAVK2UMJ6GMTMDZBDU/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":"2026-06-04T20:07:56Z","links":{"resolver":"https://pith.science/pith/2FD3IQFPOAVK2UMJ6GMTMDZBDU","bundle":"https://pith.science/pith/2FD3IQFPOAVK2UMJ6GMTMDZBDU/bundle.json","state":"https://pith.science/pith/2FD3IQFPOAVK2UMJ6GMTMDZBDU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2FD3IQFPOAVK2UMJ6GMTMDZBDU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2FD3IQFPOAVK2UMJ6GMTMDZBDU","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":"b121e3807936a403f9dc5c3f32ca209770012d2b5dc4254eea570612879790ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-01T16:19:24Z","title_canon_sha256":"f76635c283ded8931680917246d0da6e4ff5fe83d3bd697068df8712c78e964b"},"schema_version":"1.0","source":{"id":"1710.00374","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00374","created_at":"2026-05-18T00:33:54Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00374v1","created_at":"2026-05-18T00:33:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00374","created_at":"2026-05-18T00:33:54Z"},{"alias_kind":"pith_short_12","alias_value":"2FD3IQFPOAVK","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2FD3IQFPOAVK2UMJ","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2FD3IQFP","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:ff3df06e99e76f115e8b29b886154f9783d100bc8b2ed1af474d1dc08e1ba935","target":"graph","created_at":"2026-05-18T00:33:54Z","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":"An $r$-matrix is a matrix with symbols in $\\{0,1,\\ldots,r-1\\}$. A matrix is simple if it has no repeated columns. Let ${\\cal F}$ be a finite set of $r$-matrices. Let $\\hbox{forb}(m,r,{\\cal F})$ denote the maximum number of columns possible in a simple $r$-matrix\n  $A$ that has no submatrix which is a row and column permutation of any $F\\in{\\cal F}$. Many investigations have involved $r=2$. For general $r$, $\\hbox{forb}(m,r,{\\cal F})$ is polynomial in $m$ if and only if for every pair $i,j\\in\\{0,1,\\ldots,r-1\\}$ there is a matrix in ${\\cal F}$ whose entries are only $i$ or $j$.\n  Let ${\\cal T}_{","authors_text":"Attila Sali, Jeffrey Dawson, Linyuan Lu, Richard Anstee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-01T16:19:24Z","title":"Multivalued matrices and forbidden configurations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00374","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":"sha256:0280352139ee9456168eac3269f679337322dc6853d388e61c0e3d99ae1c5b40","target":"record","created_at":"2026-05-18T00:33:54Z","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":"b121e3807936a403f9dc5c3f32ca209770012d2b5dc4254eea570612879790ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-01T16:19:24Z","title_canon_sha256":"f76635c283ded8931680917246d0da6e4ff5fe83d3bd697068df8712c78e964b"},"schema_version":"1.0","source":{"id":"1710.00374","kind":"arxiv","version":1}},"canonical_sha256":"d147b440af702aad5189f199360f211d2884a26f17b36dc5fd6a7a345ff75fa8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d147b440af702aad5189f199360f211d2884a26f17b36dc5fd6a7a345ff75fa8","first_computed_at":"2026-05-18T00:33:54.976552Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:54.976552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3ezHa+bx3/In0OnZV5jpATD/qkR3qZv/pNXWjwOA61DSBw30TMYN0d8mGONqoEE3ZqnnPh2AvdLywDK5EyiRAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:54.977108Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.00374","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0280352139ee9456168eac3269f679337322dc6853d388e61c0e3d99ae1c5b40","sha256:ff3df06e99e76f115e8b29b886154f9783d100bc8b2ed1af474d1dc08e1ba935"],"state_sha256":"6710c0416c221ff792e5a990d51a129cbf41d905a62a69bf9042c93348ad8dc4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rukr6+LVc/Q9L3eFJnnRJNZYEQvJlIYY7Df/3ePpkM9rCa8YpcXqPfdP4b05vhBVdfkrQnxVOf16pd7p95B4AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T20:07:56.594576Z","bundle_sha256":"11f231cfb1a2c3d2590a5181193ee289658305b65ac9c2d0f24c93b4ca2c37c9"}}