{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:F2ZYSZDIVXPSAEPODYPRLQQVOW","short_pith_number":"pith:F2ZYSZDI","canonical_record":{"source":{"id":"1104.1776","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-10T15:20:56Z","cross_cats_sorted":[],"title_canon_sha256":"11787ead1a2af9f641a6bd8365b44e506f0239a4de39dc1e7ecca6093ad09664","abstract_canon_sha256":"0c87efdd0a34c30a88a8040fa099ede4eeebeb45a7a422cf90566ed449afb46b"},"schema_version":"1.0"},"canonical_sha256":"2eb3896468addf2011ee1e1f15c21575b97cf0a58b6111bd5ab99f8fffacf7b1","source":{"kind":"arxiv","id":"1104.1776","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1776","created_at":"2026-05-18T04:23:20Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1776v2","created_at":"2026-05-18T04:23:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1776","created_at":"2026-05-18T04:23:20Z"},{"alias_kind":"pith_short_12","alias_value":"F2ZYSZDIVXPS","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"F2ZYSZDIVXPSAEPO","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"F2ZYSZDI","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:F2ZYSZDIVXPSAEPODYPRLQQVOW","target":"record","payload":{"canonical_record":{"source":{"id":"1104.1776","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-10T15:20:56Z","cross_cats_sorted":[],"title_canon_sha256":"11787ead1a2af9f641a6bd8365b44e506f0239a4de39dc1e7ecca6093ad09664","abstract_canon_sha256":"0c87efdd0a34c30a88a8040fa099ede4eeebeb45a7a422cf90566ed449afb46b"},"schema_version":"1.0"},"canonical_sha256":"2eb3896468addf2011ee1e1f15c21575b97cf0a58b6111bd5ab99f8fffacf7b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:20.940343Z","signature_b64":"4A9Dhnf8bOZbdLL2jdNG9o7lICt72HrD8fhPn3aZpFXRTdfZQbzuR1WgPbWPaA+K8Ia52hAsk+xbwBwZiuzaDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2eb3896468addf2011ee1e1f15c21575b97cf0a58b6111bd5ab99f8fffacf7b1","last_reissued_at":"2026-05-18T04:23:20.939915Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:20.939915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.1776","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":"2026-05-18T04:23:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F2ONN4MJW4oMTFvLKKNJALYQVUuw584gCVAdJeTlYzPflNsDfS0F2faFmJj/vbMQuJotl4n5bId+9TLQ3CNnBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T01:09:43.415057Z"},"content_sha256":"16b50de2f313368a881abed0f41a10587bf8e162ac0bd4d1102cd219bff31ab1","schema_version":"1.0","event_id":"sha256:16b50de2f313368a881abed0f41a10587bf8e162ac0bd4d1102cd219bff31ab1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:F2ZYSZDIVXPSAEPODYPRLQQVOW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A proof of the set-theoretic version of the salmon conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Elizabeth Gross, Shmuel Friedland","submitted_at":"2011-04-10T15:20:56Z","abstract_excerpt":"We show that the irreducible variety of 4 x 4 x 4 complex valued tensors of border rank at most 4 is the zero set of polynomial equations of degree 5 (the Strassen commutative conditions), of degree 6 (the Landsberg-Manivel polynomials), and of degree 9 (the symmetrization conditions)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1776","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":""},"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":"2026-05-18T04:23:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VwpjBMcWISd9c6cNv2eDx6JMx0Vnyc4UCKq9h3uyYuhJ3pjEZOb05Go1XxnN8pqjU8QNmKMqqttJf3K0TkxLAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T01:09:43.415422Z"},"content_sha256":"8209ba39b39bd1640ba35bdd41d51168bc562cf179e3e71af0f80434c94d9a7c","schema_version":"1.0","event_id":"sha256:8209ba39b39bd1640ba35bdd41d51168bc562cf179e3e71af0f80434c94d9a7c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F2ZYSZDIVXPSAEPODYPRLQQVOW/bundle.json","state_url":"https://pith.science/pith/F2ZYSZDIVXPSAEPODYPRLQQVOW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F2ZYSZDIVXPSAEPODYPRLQQVOW/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":"2026-05-30T01:09:43Z","links":{"resolver":"https://pith.science/pith/F2ZYSZDIVXPSAEPODYPRLQQVOW","bundle":"https://pith.science/pith/F2ZYSZDIVXPSAEPODYPRLQQVOW/bundle.json","state":"https://pith.science/pith/F2ZYSZDIVXPSAEPODYPRLQQVOW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F2ZYSZDIVXPSAEPODYPRLQQVOW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:F2ZYSZDIVXPSAEPODYPRLQQVOW","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":"0c87efdd0a34c30a88a8040fa099ede4eeebeb45a7a422cf90566ed449afb46b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-10T15:20:56Z","title_canon_sha256":"11787ead1a2af9f641a6bd8365b44e506f0239a4de39dc1e7ecca6093ad09664"},"schema_version":"1.0","source":{"id":"1104.1776","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1776","created_at":"2026-05-18T04:23:20Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1776v2","created_at":"2026-05-18T04:23:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1776","created_at":"2026-05-18T04:23:20Z"},{"alias_kind":"pith_short_12","alias_value":"F2ZYSZDIVXPS","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"F2ZYSZDIVXPSAEPO","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"F2ZYSZDI","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:8209ba39b39bd1640ba35bdd41d51168bc562cf179e3e71af0f80434c94d9a7c","target":"graph","created_at":"2026-05-18T04:23:20Z","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":"We show that the irreducible variety of 4 x 4 x 4 complex valued tensors of border rank at most 4 is the zero set of polynomial equations of degree 5 (the Strassen commutative conditions), of degree 6 (the Landsberg-Manivel polynomials), and of degree 9 (the symmetrization conditions).","authors_text":"Elizabeth Gross, Shmuel Friedland","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-10T15:20:56Z","title":"A proof of the set-theoretic version of the salmon conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1776","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":"sha256:16b50de2f313368a881abed0f41a10587bf8e162ac0bd4d1102cd219bff31ab1","target":"record","created_at":"2026-05-18T04:23:20Z","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":"0c87efdd0a34c30a88a8040fa099ede4eeebeb45a7a422cf90566ed449afb46b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-10T15:20:56Z","title_canon_sha256":"11787ead1a2af9f641a6bd8365b44e506f0239a4de39dc1e7ecca6093ad09664"},"schema_version":"1.0","source":{"id":"1104.1776","kind":"arxiv","version":2}},"canonical_sha256":"2eb3896468addf2011ee1e1f15c21575b97cf0a58b6111bd5ab99f8fffacf7b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2eb3896468addf2011ee1e1f15c21575b97cf0a58b6111bd5ab99f8fffacf7b1","first_computed_at":"2026-05-18T04:23:20.939915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:20.939915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4A9Dhnf8bOZbdLL2jdNG9o7lICt72HrD8fhPn3aZpFXRTdfZQbzuR1WgPbWPaA+K8Ia52hAsk+xbwBwZiuzaDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:20.940343Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.1776","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16b50de2f313368a881abed0f41a10587bf8e162ac0bd4d1102cd219bff31ab1","sha256:8209ba39b39bd1640ba35bdd41d51168bc562cf179e3e71af0f80434c94d9a7c"],"state_sha256":"931d9d29764a7867c1ebd1b5c78b1dae903a1050795f47aa4871639926440292"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9PkUbTo6y7WGK0Gf+mfon8TfnuyWZr2gdb6fvx0Wljhe7+aEMHm8jZSPh6++maoGiGsc6n7e4Q1YFEjxpNixCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T01:09:43.418292Z","bundle_sha256":"041a21d118fb2c4dda1b26bc68b61ac2f2f2a0df2e8568381dc289041394e3c3"}}