{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:QX2GOWMVU3IDVZLDSF46WPM6HW","short_pith_number":"pith:QX2GOWMV","canonical_record":{"source":{"id":"2502.10007","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-02-14T08:41:57Z","cross_cats_sorted":["cs.CC","math.RT"],"title_canon_sha256":"afeacc1d5b587c27f808d0d8c9707a331ffcec1d56fa4b26bd6a8952def30155","abstract_canon_sha256":"9654d03465ff7fcf2129ac8b40b1a0cb63a80fa1a57f58d7d7b1969e11fa74d3"},"schema_version":"1.0"},"canonical_sha256":"85f4675995a6d03ae5639179eb3d9e3dbd75d3a6476fbba8f226c17f066afa8c","source":{"kind":"arxiv","id":"2502.10007","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.10007","created_at":"2026-07-05T10:14:15Z"},{"alias_kind":"arxiv_version","alias_value":"2502.10007v1","created_at":"2026-07-05T10:14:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.10007","created_at":"2026-07-05T10:14:15Z"},{"alias_kind":"pith_short_12","alias_value":"QX2GOWMVU3ID","created_at":"2026-07-05T10:14:15Z"},{"alias_kind":"pith_short_16","alias_value":"QX2GOWMVU3IDVZLD","created_at":"2026-07-05T10:14:15Z"},{"alias_kind":"pith_short_8","alias_value":"QX2GOWMV","created_at":"2026-07-05T10:14:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:QX2GOWMVU3IDVZLDSF46WPM6HW","target":"record","payload":{"canonical_record":{"source":{"id":"2502.10007","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-02-14T08:41:57Z","cross_cats_sorted":["cs.CC","math.RT"],"title_canon_sha256":"afeacc1d5b587c27f808d0d8c9707a331ffcec1d56fa4b26bd6a8952def30155","abstract_canon_sha256":"9654d03465ff7fcf2129ac8b40b1a0cb63a80fa1a57f58d7d7b1969e11fa74d3"},"schema_version":"1.0"},"canonical_sha256":"85f4675995a6d03ae5639179eb3d9e3dbd75d3a6476fbba8f226c17f066afa8c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:14:15.940509Z","signature_b64":"6u22GOfBxdzBnR40aq20oPc6Mvcf8pmY1ATKBdGXQjLUE0nVtkwEfg5Hx/Z8g+38zHs+qLRvl9VKqIe5zb76CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85f4675995a6d03ae5639179eb3d9e3dbd75d3a6476fbba8f226c17f066afa8c","last_reissued_at":"2026-07-05T10:14:15.940002Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:14:15.940002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.10007","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":"2026-07-05T10:14:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oKrjK4TtPXDf2qtIV62UG/q5y76rvLVc1sITPh89mnbkkC+X5q11ahBKpb7PLEXANbXvk2TX87VckA1fyB+OBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T19:21:18.500147Z"},"content_sha256":"90bfd5eb9a4f135eaacda1b023366119950170aa665b3f2f1f0f0d1c9af2e6f3","schema_version":"1.0","event_id":"sha256:90bfd5eb9a4f135eaacda1b023366119950170aa665b3f2f1f0f0d1c9af2e6f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:QX2GOWMVU3IDVZLDSF46WPM6HW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strength and partition rank under limits and field extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.RT"],"primary_cat":"math.AG","authors_text":"Amichai Lampert, Arthur Bik, Jan Draisma, Tamar Ziegler","submitted_at":"2025-02-14T08:41:57Z","abstract_excerpt":"The strength of a multivariate homogeneous polynomial is the minimal number of terms in an expression as a sum of products of lower-degree homogeneous polynomials. Partition rank is the analogue for multilinear forms. Both ranks can drop under field extensions, and both can jump in a limit. We show that, for fixed degree and under mild conditions on the characteristic of the ground field, the strength is at most a polynomial in the border strength. We also establish an analogous result for partition rank. Our results control both the jump under limits and the drop under field extensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.10007","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.10007/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":"2026-07-05T10:14:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AhRCQ+XNcyw4z6R22Lyk+ppwELWQImiWpJAcy8G4nE+A5Jue1ZH4cwLYtKSaeOtP21JclLnKN5mZkFVHtHeZDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T19:21:18.500759Z"},"content_sha256":"bcb14f464402af9059f020a9620fc90a4fef0c2a26ad470d1b47d0496aa8f34c","schema_version":"1.0","event_id":"sha256:bcb14f464402af9059f020a9620fc90a4fef0c2a26ad470d1b47d0496aa8f34c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QX2GOWMVU3IDVZLDSF46WPM6HW/bundle.json","state_url":"https://pith.science/pith/QX2GOWMVU3IDVZLDSF46WPM6HW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QX2GOWMVU3IDVZLDSF46WPM6HW/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":"2026-08-08T19:21:18Z","links":{"resolver":"https://pith.science/pith/QX2GOWMVU3IDVZLDSF46WPM6HW","bundle":"https://pith.science/pith/QX2GOWMVU3IDVZLDSF46WPM6HW/bundle.json","state":"https://pith.science/pith/QX2GOWMVU3IDVZLDSF46WPM6HW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QX2GOWMVU3IDVZLDSF46WPM6HW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QX2GOWMVU3IDVZLDSF46WPM6HW","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":"9654d03465ff7fcf2129ac8b40b1a0cb63a80fa1a57f58d7d7b1969e11fa74d3","cross_cats_sorted":["cs.CC","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-02-14T08:41:57Z","title_canon_sha256":"afeacc1d5b587c27f808d0d8c9707a331ffcec1d56fa4b26bd6a8952def30155"},"schema_version":"1.0","source":{"id":"2502.10007","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.10007","created_at":"2026-07-05T10:14:15Z"},{"alias_kind":"arxiv_version","alias_value":"2502.10007v1","created_at":"2026-07-05T10:14:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.10007","created_at":"2026-07-05T10:14:15Z"},{"alias_kind":"pith_short_12","alias_value":"QX2GOWMVU3ID","created_at":"2026-07-05T10:14:15Z"},{"alias_kind":"pith_short_16","alias_value":"QX2GOWMVU3IDVZLD","created_at":"2026-07-05T10:14:15Z"},{"alias_kind":"pith_short_8","alias_value":"QX2GOWMV","created_at":"2026-07-05T10:14:15Z"}],"graph_snapshots":[{"event_id":"sha256:bcb14f464402af9059f020a9620fc90a4fef0c2a26ad470d1b47d0496aa8f34c","target":"graph","created_at":"2026-07-05T10:14:15Z","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/2502.10007/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The strength of a multivariate homogeneous polynomial is the minimal number of terms in an expression as a sum of products of lower-degree homogeneous polynomials. Partition rank is the analogue for multilinear forms. Both ranks can drop under field extensions, and both can jump in a limit. We show that, for fixed degree and under mild conditions on the characteristic of the ground field, the strength is at most a polynomial in the border strength. We also establish an analogous result for partition rank. Our results control both the jump under limits and the drop under field extensions.","authors_text":"Amichai Lampert, Arthur Bik, Jan Draisma, Tamar Ziegler","cross_cats":["cs.CC","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-02-14T08:41:57Z","title":"Strength and partition rank under limits and field extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.10007","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":"sha256:90bfd5eb9a4f135eaacda1b023366119950170aa665b3f2f1f0f0d1c9af2e6f3","target":"record","created_at":"2026-07-05T10:14:15Z","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":"9654d03465ff7fcf2129ac8b40b1a0cb63a80fa1a57f58d7d7b1969e11fa74d3","cross_cats_sorted":["cs.CC","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-02-14T08:41:57Z","title_canon_sha256":"afeacc1d5b587c27f808d0d8c9707a331ffcec1d56fa4b26bd6a8952def30155"},"schema_version":"1.0","source":{"id":"2502.10007","kind":"arxiv","version":1}},"canonical_sha256":"85f4675995a6d03ae5639179eb3d9e3dbd75d3a6476fbba8f226c17f066afa8c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85f4675995a6d03ae5639179eb3d9e3dbd75d3a6476fbba8f226c17f066afa8c","first_computed_at":"2026-07-05T10:14:15.940002Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:14:15.940002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6u22GOfBxdzBnR40aq20oPc6Mvcf8pmY1ATKBdGXQjLUE0nVtkwEfg5Hx/Z8g+38zHs+qLRvl9VKqIe5zb76CA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:14:15.940509Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.10007","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90bfd5eb9a4f135eaacda1b023366119950170aa665b3f2f1f0f0d1c9af2e6f3","sha256:bcb14f464402af9059f020a9620fc90a4fef0c2a26ad470d1b47d0496aa8f34c"],"state_sha256":"6fd67f43cfe0443d2de45af52feb3b8e75bc177cff48056ccdbdb41f553342f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xBPm2GbFNaSnul+Z6x0vFmvSJEY1DHnNEDJVy5vzsnOQCgdtXY3BRpTUDLsCklxwNs2Bf1vg32kjLMlW3s0ABQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T19:21:18.510478Z","bundle_sha256":"4ea3c2c44f528ece458ce386364bcfa0270443116cf553bf79b7c612c60713dd"}}