{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:CT2MW6NEBQVYZIFCD7JCDMXUZV","short_pith_number":"pith:CT2MW6NE","canonical_record":{"source":{"id":"2606.24529","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-23T12:58:17Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"7e5b542b9f8e692991e52bb5ff76a785695352b9cc9cda9b61eaeea3a324c038","abstract_canon_sha256":"e0dbd1bfdd33361f359e455a6bc62ae102ce3badcb9ac3788a5d9ebd9ec942ea"},"schema_version":"1.0"},"canonical_sha256":"14f4cb79a40c2b8ca0a21fd221b2f4cd75a4c662a0e5fb7002059d6683d1a5d1","source":{"kind":"arxiv","id":"2606.24529","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.24529","created_at":"2026-06-24T01:15:33Z"},{"alias_kind":"arxiv_version","alias_value":"2606.24529v1","created_at":"2026-06-24T01:15:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.24529","created_at":"2026-06-24T01:15:33Z"},{"alias_kind":"pith_short_12","alias_value":"CT2MW6NEBQVY","created_at":"2026-06-24T01:15:33Z"},{"alias_kind":"pith_short_16","alias_value":"CT2MW6NEBQVYZIFC","created_at":"2026-06-24T01:15:33Z"},{"alias_kind":"pith_short_8","alias_value":"CT2MW6NE","created_at":"2026-06-24T01:15:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:CT2MW6NEBQVYZIFCD7JCDMXUZV","target":"record","payload":{"canonical_record":{"source":{"id":"2606.24529","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-23T12:58:17Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"7e5b542b9f8e692991e52bb5ff76a785695352b9cc9cda9b61eaeea3a324c038","abstract_canon_sha256":"e0dbd1bfdd33361f359e455a6bc62ae102ce3badcb9ac3788a5d9ebd9ec942ea"},"schema_version":"1.0"},"canonical_sha256":"14f4cb79a40c2b8ca0a21fd221b2f4cd75a4c662a0e5fb7002059d6683d1a5d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-24T01:15:33.078458Z","signature_b64":"jFKN6QA655QVLtNCq7h3oAeQaGdnHQWtPVmy/4bDsiONxz0OdYIAYpe24yBVRTAjzYLXMW/GsIbbKuXb9+XbDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14f4cb79a40c2b8ca0a21fd221b2f4cd75a4c662a0e5fb7002059d6683d1a5d1","last_reissued_at":"2026-06-24T01:15:33.078021Z","signature_status":"signed_v1","first_computed_at":"2026-06-24T01:15:33.078021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.24529","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":"2026-06-24T01:15:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ncTdH4EphEExafCLszpGG2E49iPTCY6sLHorAFRf6X24nGiFuWCU06YKSnkQWtKqRKlflAMFdCqAVYZuTi1oCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T05:21:37.148547Z"},"content_sha256":"6dc45f6243f41b0aeb051f9d67630b3bbabfb39136f9aa962dac0daa35621fe9","schema_version":"1.0","event_id":"sha256:6dc45f6243f41b0aeb051f9d67630b3bbabfb39136f9aa962dac0daa35621fe9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:CT2MW6NEBQVYZIFCD7JCDMXUZV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Erd\\H{o}s Matching Conjecture for Vector Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Baoyan Feng, Chenyang Zhang, Chong Shangguan, Yulin Yang","submitted_at":"2026-06-23T12:58:17Z","abstract_excerpt":"We study a vector-space analogue of the Erd\\H{o}s Matching Conjecture. Let $m_q(n,k,s)$ denote the maximum cardinality of a family of $k$-dimensional subspaces of an $n$-dimensional vector space over $\\mathbb F_q$ with no $s+1$ members whose sum is direct. Two natural constructions provide lower bounds. The first consists of all $k$-subspaces contained in a fixed $((s+1)k-1)$-dimensional subspace; the second consists of all $k$-subspaces that intersect a fixed $s$-dimensional subspace nontrivially. These constructions motivate the following vector-space analogue of the Erd\\H{o}s Matching Conje"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24529","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/2606.24529/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":"2026-06-24T01:15:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZX8RGidMNHb4re2aEcFwpRrSeCcH8pQ8VKOdNsjjRzs2MMgk3PQwub6Rps94pi0ruGSuHqYWSes3R6RrMImHBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T05:21:37.148913Z"},"content_sha256":"55e2d73a5d0738c6c67ee93490bacaaca855ea8f39796ea86b3f05f110303a8b","schema_version":"1.0","event_id":"sha256:55e2d73a5d0738c6c67ee93490bacaaca855ea8f39796ea86b3f05f110303a8b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CT2MW6NEBQVYZIFCD7JCDMXUZV/bundle.json","state_url":"https://pith.science/pith/CT2MW6NEBQVYZIFCD7JCDMXUZV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CT2MW6NEBQVYZIFCD7JCDMXUZV/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":"2026-06-29T05:21:37Z","links":{"resolver":"https://pith.science/pith/CT2MW6NEBQVYZIFCD7JCDMXUZV","bundle":"https://pith.science/pith/CT2MW6NEBQVYZIFCD7JCDMXUZV/bundle.json","state":"https://pith.science/pith/CT2MW6NEBQVYZIFCD7JCDMXUZV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CT2MW6NEBQVYZIFCD7JCDMXUZV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CT2MW6NEBQVYZIFCD7JCDMXUZV","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":"e0dbd1bfdd33361f359e455a6bc62ae102ce3badcb9ac3788a5d9ebd9ec942ea","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-23T12:58:17Z","title_canon_sha256":"7e5b542b9f8e692991e52bb5ff76a785695352b9cc9cda9b61eaeea3a324c038"},"schema_version":"1.0","source":{"id":"2606.24529","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.24529","created_at":"2026-06-24T01:15:33Z"},{"alias_kind":"arxiv_version","alias_value":"2606.24529v1","created_at":"2026-06-24T01:15:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.24529","created_at":"2026-06-24T01:15:33Z"},{"alias_kind":"pith_short_12","alias_value":"CT2MW6NEBQVY","created_at":"2026-06-24T01:15:33Z"},{"alias_kind":"pith_short_16","alias_value":"CT2MW6NEBQVYZIFC","created_at":"2026-06-24T01:15:33Z"},{"alias_kind":"pith_short_8","alias_value":"CT2MW6NE","created_at":"2026-06-24T01:15:33Z"}],"graph_snapshots":[{"event_id":"sha256:55e2d73a5d0738c6c67ee93490bacaaca855ea8f39796ea86b3f05f110303a8b","target":"graph","created_at":"2026-06-24T01:15:33Z","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/2606.24529/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a vector-space analogue of the Erd\\H{o}s Matching Conjecture. Let $m_q(n,k,s)$ denote the maximum cardinality of a family of $k$-dimensional subspaces of an $n$-dimensional vector space over $\\mathbb F_q$ with no $s+1$ members whose sum is direct. Two natural constructions provide lower bounds. The first consists of all $k$-subspaces contained in a fixed $((s+1)k-1)$-dimensional subspace; the second consists of all $k$-subspaces that intersect a fixed $s$-dimensional subspace nontrivially. These constructions motivate the following vector-space analogue of the Erd\\H{o}s Matching Conje","authors_text":"Baoyan Feng, Chenyang Zhang, Chong Shangguan, Yulin Yang","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-23T12:58:17Z","title":"An Erd\\H{o}s Matching Conjecture for Vector Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24529","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":"sha256:6dc45f6243f41b0aeb051f9d67630b3bbabfb39136f9aa962dac0daa35621fe9","target":"record","created_at":"2026-06-24T01:15:33Z","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":"e0dbd1bfdd33361f359e455a6bc62ae102ce3badcb9ac3788a5d9ebd9ec942ea","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-23T12:58:17Z","title_canon_sha256":"7e5b542b9f8e692991e52bb5ff76a785695352b9cc9cda9b61eaeea3a324c038"},"schema_version":"1.0","source":{"id":"2606.24529","kind":"arxiv","version":1}},"canonical_sha256":"14f4cb79a40c2b8ca0a21fd221b2f4cd75a4c662a0e5fb7002059d6683d1a5d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14f4cb79a40c2b8ca0a21fd221b2f4cd75a4c662a0e5fb7002059d6683d1a5d1","first_computed_at":"2026-06-24T01:15:33.078021Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-24T01:15:33.078021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jFKN6QA655QVLtNCq7h3oAeQaGdnHQWtPVmy/4bDsiONxz0OdYIAYpe24yBVRTAjzYLXMW/GsIbbKuXb9+XbDg==","signature_status":"signed_v1","signed_at":"2026-06-24T01:15:33.078458Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.24529","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6dc45f6243f41b0aeb051f9d67630b3bbabfb39136f9aa962dac0daa35621fe9","sha256:55e2d73a5d0738c6c67ee93490bacaaca855ea8f39796ea86b3f05f110303a8b"],"state_sha256":"63a2ec3bb2d7335986e1e1e7448c8541e467afb6c4d6af819ba86c8a512d86bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hlIqBVa05vDXqFDcpbr0P8e19R8nE5HN4GQlRBmJY4wmP6Z4dZ+/BTTBT/tIF7bOaU+3W3TwNXehP2BpXu3mDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T05:21:37.150882Z","bundle_sha256":"a6bf4f2dda625a6194a21ce2bbc0115f4a7ae230905e7abbe2bdaaf7dcc3e80a"}}