{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ZXHLRFF5AZLQB24LQEUVOHLCD6","short_pith_number":"pith:ZXHLRFF5","canonical_record":{"source":{"id":"1709.07851","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-22T17:07:59Z","cross_cats_sorted":["cs.CC","quant-ph"],"title_canon_sha256":"6f9b24d1c76308c05252a8f8439cb360ec4162fc0933d900570dd2bc4110a637","abstract_canon_sha256":"1ceadf0604bec311c5b9cb1d34ff959c9076f15353e10bdeb759b8f0b823ab57"},"schema_version":"1.0"},"canonical_sha256":"cdceb894bd065700eb8b8129571d621f8c87735db2686d7541b56def7da89430","source":{"kind":"arxiv","id":"1709.07851","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.07851","created_at":"2026-07-05T05:17:22Z"},{"alias_kind":"arxiv_version","alias_value":"1709.07851v3","created_at":"2026-07-05T05:17:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.07851","created_at":"2026-07-05T05:17:22Z"},{"alias_kind":"pith_short_12","alias_value":"ZXHLRFF5AZLQ","created_at":"2026-07-05T05:17:22Z"},{"alias_kind":"pith_short_16","alias_value":"ZXHLRFF5AZLQB24L","created_at":"2026-07-05T05:17:22Z"},{"alias_kind":"pith_short_8","alias_value":"ZXHLRFF5","created_at":"2026-07-05T05:17:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ZXHLRFF5AZLQB24LQEUVOHLCD6","target":"record","payload":{"canonical_record":{"source":{"id":"1709.07851","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-22T17:07:59Z","cross_cats_sorted":["cs.CC","quant-ph"],"title_canon_sha256":"6f9b24d1c76308c05252a8f8439cb360ec4162fc0933d900570dd2bc4110a637","abstract_canon_sha256":"1ceadf0604bec311c5b9cb1d34ff959c9076f15353e10bdeb759b8f0b823ab57"},"schema_version":"1.0"},"canonical_sha256":"cdceb894bd065700eb8b8129571d621f8c87735db2686d7541b56def7da89430","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:17:22.371767Z","signature_b64":"yoQdmNK+J6HAQ+XD56647XgMPpCwC+UWC+Xy1kSHHfRIyTaeljf7j1OhU36ymzYtB0gdbe97o6XLA7BAamRuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cdceb894bd065700eb8b8129571d621f8c87735db2686d7541b56def7da89430","last_reissued_at":"2026-07-05T05:17:22.371278Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:17:22.371278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.07851","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:17:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"syl6XzKpwvI6c/Mv2rolZx4Bfoe/hFHWSiywzoIETWZ41ZfCEesp5jTMY22KNKuYvzElLqDs+4Xx6p+CCLVYBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T03:15:48.515057Z"},"content_sha256":"446c8b4c36f279152836f5f1195fa9c96bcbbea7bf8493c646e365204fb910d7","schema_version":"1.0","event_id":"sha256:446c8b4c36f279152836f5f1195fa9c96bcbbea7bf8493c646e365204fb910d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ZXHLRFF5AZLQB24LQEUVOHLCD6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universal points in the asymptotic spectrum of tensors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","quant-ph"],"primary_cat":"math.CO","authors_text":"Jeroen Zuiddam, Matthias Christandl, P\\'eter Vrana","submitted_at":"2017-09-22T17:07:59Z","abstract_excerpt":"The asymptotic restriction problem for tensors is to decide, given tensors $s$ and $t$, whether the nth tensor power of $s$ can be obtained from the $(n+o(n))$th tensor power of t by applying linear maps to the tensor legs (this we call restriction), when $n$ goes to infinity. In this context, Volker Strassen, striving to understand the complexity of matrix multiplication, introduced in 1986 the asymptotic spectrum of tensors. Essentially, the asymptotic restriction problem for a family of tensors $X$, closed under direct sum and tensor product, reduces to finding all maps from $X$ to the real"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.07851","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1709.07851/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:17:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H1vpjoHPEsGeFlF8BYshWF/d8mbZNP6BT22/E/G5SW9qfrnZ/i2RTKEMXwUWlxvApq9Xfp7yIWAtI077zhG0BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T03:15:48.515597Z"},"content_sha256":"ffb1ed70a7d0fdc416ca68ca4dd3bc940829cc761dc181835040ce67644dff5a","schema_version":"1.0","event_id":"sha256:ffb1ed70a7d0fdc416ca68ca4dd3bc940829cc761dc181835040ce67644dff5a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZXHLRFF5AZLQB24LQEUVOHLCD6/bundle.json","state_url":"https://pith.science/pith/ZXHLRFF5AZLQB24LQEUVOHLCD6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZXHLRFF5AZLQB24LQEUVOHLCD6/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":"2026-08-11T03:15:48Z","links":{"resolver":"https://pith.science/pith/ZXHLRFF5AZLQB24LQEUVOHLCD6","bundle":"https://pith.science/pith/ZXHLRFF5AZLQB24LQEUVOHLCD6/bundle.json","state":"https://pith.science/pith/ZXHLRFF5AZLQB24LQEUVOHLCD6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZXHLRFF5AZLQB24LQEUVOHLCD6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZXHLRFF5AZLQB24LQEUVOHLCD6","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":"1ceadf0604bec311c5b9cb1d34ff959c9076f15353e10bdeb759b8f0b823ab57","cross_cats_sorted":["cs.CC","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-22T17:07:59Z","title_canon_sha256":"6f9b24d1c76308c05252a8f8439cb360ec4162fc0933d900570dd2bc4110a637"},"schema_version":"1.0","source":{"id":"1709.07851","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.07851","created_at":"2026-07-05T05:17:22Z"},{"alias_kind":"arxiv_version","alias_value":"1709.07851v3","created_at":"2026-07-05T05:17:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.07851","created_at":"2026-07-05T05:17:22Z"},{"alias_kind":"pith_short_12","alias_value":"ZXHLRFF5AZLQ","created_at":"2026-07-05T05:17:22Z"},{"alias_kind":"pith_short_16","alias_value":"ZXHLRFF5AZLQB24L","created_at":"2026-07-05T05:17:22Z"},{"alias_kind":"pith_short_8","alias_value":"ZXHLRFF5","created_at":"2026-07-05T05:17:22Z"}],"graph_snapshots":[{"event_id":"sha256:ffb1ed70a7d0fdc416ca68ca4dd3bc940829cc761dc181835040ce67644dff5a","target":"graph","created_at":"2026-07-05T05:17:22Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1709.07851/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The asymptotic restriction problem for tensors is to decide, given tensors $s$ and $t$, whether the nth tensor power of $s$ can be obtained from the $(n+o(n))$th tensor power of t by applying linear maps to the tensor legs (this we call restriction), when $n$ goes to infinity. In this context, Volker Strassen, striving to understand the complexity of matrix multiplication, introduced in 1986 the asymptotic spectrum of tensors. Essentially, the asymptotic restriction problem for a family of tensors $X$, closed under direct sum and tensor product, reduces to finding all maps from $X$ to the real","authors_text":"Jeroen Zuiddam, Matthias Christandl, P\\'eter Vrana","cross_cats":["cs.CC","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-22T17:07:59Z","title":"Universal points in the asymptotic spectrum of tensors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.07851","kind":"arxiv","version":3},"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":"sha256:446c8b4c36f279152836f5f1195fa9c96bcbbea7bf8493c646e365204fb910d7","target":"record","created_at":"2026-07-05T05:17:22Z","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":"1ceadf0604bec311c5b9cb1d34ff959c9076f15353e10bdeb759b8f0b823ab57","cross_cats_sorted":["cs.CC","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-22T17:07:59Z","title_canon_sha256":"6f9b24d1c76308c05252a8f8439cb360ec4162fc0933d900570dd2bc4110a637"},"schema_version":"1.0","source":{"id":"1709.07851","kind":"arxiv","version":3}},"canonical_sha256":"cdceb894bd065700eb8b8129571d621f8c87735db2686d7541b56def7da89430","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cdceb894bd065700eb8b8129571d621f8c87735db2686d7541b56def7da89430","first_computed_at":"2026-07-05T05:17:22.371278Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:17:22.371278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yoQdmNK+J6HAQ+XD56647XgMPpCwC+UWC+Xy1kSHHfRIyTaeljf7j1OhU36ymzYtB0gdbe97o6XLA7BAamRuCw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:17:22.371767Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.07851","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:446c8b4c36f279152836f5f1195fa9c96bcbbea7bf8493c646e365204fb910d7","sha256:ffb1ed70a7d0fdc416ca68ca4dd3bc940829cc761dc181835040ce67644dff5a"],"state_sha256":"1e3b8c70141a584cd1578388be5dbc2128e3dd23a3188af2f8b007ce18db3742"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UcOHrdBR+FOUuxvSW040TvOh2Jevx9QY2+3Gx6zdk8TF/1aJWRn5OAFf3uwrKVfvR2oVjnPLQ/D/+eujVwlqAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T03:15:48.521311Z","bundle_sha256":"e6bc824e5d1e428d80474784b5e79cac60a797b574bbac7d44ff19281a4cd07c"}}