{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1995:KO6MCU2MHGNVJSNYTMPZYABZLK","short_pith_number":"pith:KO6MCU2M","canonical_record":{"source":{"id":"math/9510215","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.LO","submitted_at":"1995-10-15T00:00:00Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"855e4c47abc1a70f5ec0a1b9e05703e103bd7c3a4fa87774d418459ed0654141","abstract_canon_sha256":"7688042c55ae645fd9107164e7b6639c957611fa4a484d836b1435e06d25ef29"},"schema_version":"1.0"},"canonical_sha256":"53bcc1534c399b54c9b89b1f9c00395a83e96550c177f1dc3fdc4802589e43fa","source":{"kind":"arxiv","id":"math/9510215","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9510215","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"arxiv_version","alias_value":"math/9510215v1","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9510215","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"pith_short_12","alias_value":"KO6MCU2MHGNV","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"KO6MCU2MHGNVJSNY","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"KO6MCU2M","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1995:KO6MCU2MHGNVJSNYTMPZYABZLK","target":"record","payload":{"canonical_record":{"source":{"id":"math/9510215","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.LO","submitted_at":"1995-10-15T00:00:00Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"855e4c47abc1a70f5ec0a1b9e05703e103bd7c3a4fa87774d418459ed0654141","abstract_canon_sha256":"7688042c55ae645fd9107164e7b6639c957611fa4a484d836b1435e06d25ef29"},"schema_version":"1.0"},"canonical_sha256":"53bcc1534c399b54c9b89b1f9c00395a83e96550c177f1dc3fdc4802589e43fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:48.201269Z","signature_b64":"MJi7kGOT+63Obt55ncdvCmWDBiy9MmvUt6o8U3nR5QQCgQaSCsjHP02i+E8Vo/xFkmrn2bfEKSJVpdiFfzHhBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53bcc1534c399b54c9b89b1f9c00395a83e96550c177f1dc3fdc4802589e43fa","last_reissued_at":"2026-05-18T01:05:48.200789Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:48.200789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9510215","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":"2026-05-18T01:05:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ym8gKMfiRU3ASR+P0Abj/27HZyjJU8P4PgVJAnRfopxwQMf0uYQFKxdB2vsu1sbMsNreSFuv5hDB2uyCMahVCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:12:00.638423Z"},"content_sha256":"5de22ddafbe641bb9872e40e5f66bfd8eb8b40a540056d8217b8770394a4503a","schema_version":"1.0","event_id":"sha256:5de22ddafbe641bb9872e40e5f66bfd8eb8b40a540056d8217b8770394a4503a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1995:KO6MCU2MHGNVJSNYTMPZYABZLK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Gross spaces","license":"","headline":"","cross_cats":["math.RA"],"primary_cat":"math.LO","authors_text":"Otmar Spinas, Saharon Shelah","submitted_at":"1995-10-15T00:00:00Z","abstract_excerpt":"A Gross space is a vector space E of infinite dimension over some field F, which is endowed with a symmetric bilinear form Phi:E^2 -> F and has the property that every infinite dimensional subspace U subseteq E satisfies dim U^perp < dim E. Gross spaces over uncountable fields exist (in certain dimensions). The existence of a Gross space over countable or finite fields (in a fixed dimension not above the continuum) is independent of the axioms of ZFC. Here we continue the investigation of Gross spaces. Among other things we show that if the cardinal invariant b equals omega_1 a Gross space in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9510215","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":"2026-05-18T01:05:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"12Za2KG8p1ApMEAc6lj6lFLVs2mlALInDDBexq5y/NImNlsM1rpDr0NURE42YzX0QIXIrgd7E4+0jEZIJWmnAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:12:00.639123Z"},"content_sha256":"e02f714781b44a53e64830093616482bf57fd0d7f02084e42dff5a815febacec","schema_version":"1.0","event_id":"sha256:e02f714781b44a53e64830093616482bf57fd0d7f02084e42dff5a815febacec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KO6MCU2MHGNVJSNYTMPZYABZLK/bundle.json","state_url":"https://pith.science/pith/KO6MCU2MHGNVJSNYTMPZYABZLK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KO6MCU2MHGNVJSNYTMPZYABZLK/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":"2026-06-09T06:12:00Z","links":{"resolver":"https://pith.science/pith/KO6MCU2MHGNVJSNYTMPZYABZLK","bundle":"https://pith.science/pith/KO6MCU2MHGNVJSNYTMPZYABZLK/bundle.json","state":"https://pith.science/pith/KO6MCU2MHGNVJSNYTMPZYABZLK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KO6MCU2MHGNVJSNYTMPZYABZLK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1995:KO6MCU2MHGNVJSNYTMPZYABZLK","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":"7688042c55ae645fd9107164e7b6639c957611fa4a484d836b1435e06d25ef29","cross_cats_sorted":["math.RA"],"license":"","primary_cat":"math.LO","submitted_at":"1995-10-15T00:00:00Z","title_canon_sha256":"855e4c47abc1a70f5ec0a1b9e05703e103bd7c3a4fa87774d418459ed0654141"},"schema_version":"1.0","source":{"id":"math/9510215","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9510215","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"arxiv_version","alias_value":"math/9510215v1","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9510215","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"pith_short_12","alias_value":"KO6MCU2MHGNV","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"KO6MCU2MHGNVJSNY","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"KO6MCU2M","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:e02f714781b44a53e64830093616482bf57fd0d7f02084e42dff5a815febacec","target":"graph","created_at":"2026-05-18T01:05:48Z","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":"A Gross space is a vector space E of infinite dimension over some field F, which is endowed with a symmetric bilinear form Phi:E^2 -> F and has the property that every infinite dimensional subspace U subseteq E satisfies dim U^perp < dim E. Gross spaces over uncountable fields exist (in certain dimensions). The existence of a Gross space over countable or finite fields (in a fixed dimension not above the continuum) is independent of the axioms of ZFC. Here we continue the investigation of Gross spaces. Among other things we show that if the cardinal invariant b equals omega_1 a Gross space in ","authors_text":"Otmar Spinas, Saharon Shelah","cross_cats":["math.RA"],"headline":"","license":"","primary_cat":"math.LO","submitted_at":"1995-10-15T00:00:00Z","title":"On Gross spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9510215","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":"sha256:5de22ddafbe641bb9872e40e5f66bfd8eb8b40a540056d8217b8770394a4503a","target":"record","created_at":"2026-05-18T01:05:48Z","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":"7688042c55ae645fd9107164e7b6639c957611fa4a484d836b1435e06d25ef29","cross_cats_sorted":["math.RA"],"license":"","primary_cat":"math.LO","submitted_at":"1995-10-15T00:00:00Z","title_canon_sha256":"855e4c47abc1a70f5ec0a1b9e05703e103bd7c3a4fa87774d418459ed0654141"},"schema_version":"1.0","source":{"id":"math/9510215","kind":"arxiv","version":1}},"canonical_sha256":"53bcc1534c399b54c9b89b1f9c00395a83e96550c177f1dc3fdc4802589e43fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53bcc1534c399b54c9b89b1f9c00395a83e96550c177f1dc3fdc4802589e43fa","first_computed_at":"2026-05-18T01:05:48.200789Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:48.200789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MJi7kGOT+63Obt55ncdvCmWDBiy9MmvUt6o8U3nR5QQCgQaSCsjHP02i+E8Vo/xFkmrn2bfEKSJVpdiFfzHhBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:48.201269Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9510215","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5de22ddafbe641bb9872e40e5f66bfd8eb8b40a540056d8217b8770394a4503a","sha256:e02f714781b44a53e64830093616482bf57fd0d7f02084e42dff5a815febacec"],"state_sha256":"af88a72021f0eeb9a06f5aeb0d4ef2f73d6f872815d4a6090f64ea7abdaca96a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kpf6v1MZEjPgBFy2xrsOcRi0JdmBTUEc9kU8HbdY+n8MeNIpr+hK0H2W4cFbMzmENGCRdOxZCos+WKSwChoxBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T06:12:00.643006Z","bundle_sha256":"d24461f866b2f083ec63254b94989f63b76aa76d67ec9bf48f259e59df359924"}}