{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1995:LRGBQDAXJ3FLMOJ6SQIU4DJ5PV","short_pith_number":"pith:LRGBQDAX","canonical_record":{"source":{"id":"math/9507212","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.LO","submitted_at":"1995-07-24T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"a9708ddecdc5e86eac98e764a69f9ea9f5002b372441bdfdc0f85c1cd8d3b7ab","abstract_canon_sha256":"73cedb7915392db05f0d24d6e236c024087e82561d8cfc45d7d53b856642106c"},"schema_version":"1.0"},"canonical_sha256":"5c4c180c174ecab6393e94114e0d3d7d570e47f8b3ee15a7fad68db87be41203","source":{"kind":"arxiv","id":"math/9507212","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9507212","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"arxiv_version","alias_value":"math/9507212v1","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9507212","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"pith_short_12","alias_value":"LRGBQDAXJ3FL","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"LRGBQDAXJ3FLMOJ6","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"LRGBQDAX","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1995:LRGBQDAXJ3FLMOJ6SQIU4DJ5PV","target":"record","payload":{"canonical_record":{"source":{"id":"math/9507212","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.LO","submitted_at":"1995-07-24T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"a9708ddecdc5e86eac98e764a69f9ea9f5002b372441bdfdc0f85c1cd8d3b7ab","abstract_canon_sha256":"73cedb7915392db05f0d24d6e236c024087e82561d8cfc45d7d53b856642106c"},"schema_version":"1.0"},"canonical_sha256":"5c4c180c174ecab6393e94114e0d3d7d570e47f8b3ee15a7fad68db87be41203","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:48.503725Z","signature_b64":"njTZnop+zEVPPX7KMZUZuEzxz6H0nrMDJ+Aebrh3vNhn10v5I7ZapiNUGQBPdI+B8JgBnqMAiXMQGdwtPUY9DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c4c180c174ecab6393e94114e0d3d7d570e47f8b3ee15a7fad68db87be41203","last_reissued_at":"2026-05-18T01:05:48.503293Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:48.503293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9507212","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":"cjxCHTGDOiUkDzTmQTHj90dMR/bmYtvOdYBNAps4xMgDyLjUBi8j2IdbRceFH7XegDprUVtWhr9QFEP9KrmMAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T17:03:47.221891Z"},"content_sha256":"64a7876994e7714834be3ab09313f71ad43b79815b3d5eccfde70350f63d13aa","schema_version":"1.0","event_id":"sha256:64a7876994e7714834be3ab09313f71ad43b79815b3d5eccfde70350f63d13aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1995:LRGBQDAXJ3FLMOJ6SQIU4DJ5PV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Representing embeddability as set inclusion","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Menachem Kojman","submitted_at":"1995-07-24T00:00:00Z","abstract_excerpt":"A few steps are made towards representation theory of embeddability among uncountable graphs. A monotone class of graphs is defined by forbidding countable subgraphs, related to the graph's end-structure. Using a combinatorial theorem of Shelah it is proved:\n - The complexity of the class in every regular uncountable $\\l>\\aleph_1$ is at least $\\lambda^+ + \\sup\\{\\mu^{\\aleph_0}:\\mu^+<\\lambda\\}$\n - For all regular uncountable $\\lambda>\\aleph_1$ there are $2^\\lambda$ pairwise non embeddable graphs in the class having strong homogeneity properties.\n - It is characterized when some invariants of a g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9507212","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":"rsUrpxQ0FV845y8CxO1lXk7enwo+IFJHororM4DC9DoA+PlZYt68pGfBd1am3PYLFjfO6FMg0ZKB4IHs+I8dDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T17:03:47.222236Z"},"content_sha256":"164a5778dbfa2664aa84cc35ea785c2b2f99b5e7b8cc61e6637d42eb8bd3cf21","schema_version":"1.0","event_id":"sha256:164a5778dbfa2664aa84cc35ea785c2b2f99b5e7b8cc61e6637d42eb8bd3cf21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LRGBQDAXJ3FLMOJ6SQIU4DJ5PV/bundle.json","state_url":"https://pith.science/pith/LRGBQDAXJ3FLMOJ6SQIU4DJ5PV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LRGBQDAXJ3FLMOJ6SQIU4DJ5PV/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":"2026-06-22T17:03:47Z","links":{"resolver":"https://pith.science/pith/LRGBQDAXJ3FLMOJ6SQIU4DJ5PV","bundle":"https://pith.science/pith/LRGBQDAXJ3FLMOJ6SQIU4DJ5PV/bundle.json","state":"https://pith.science/pith/LRGBQDAXJ3FLMOJ6SQIU4DJ5PV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LRGBQDAXJ3FLMOJ6SQIU4DJ5PV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1995:LRGBQDAXJ3FLMOJ6SQIU4DJ5PV","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":"73cedb7915392db05f0d24d6e236c024087e82561d8cfc45d7d53b856642106c","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"1995-07-24T00:00:00Z","title_canon_sha256":"a9708ddecdc5e86eac98e764a69f9ea9f5002b372441bdfdc0f85c1cd8d3b7ab"},"schema_version":"1.0","source":{"id":"math/9507212","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9507212","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"arxiv_version","alias_value":"math/9507212v1","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9507212","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"pith_short_12","alias_value":"LRGBQDAXJ3FL","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"LRGBQDAXJ3FLMOJ6","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"LRGBQDAX","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:164a5778dbfa2664aa84cc35ea785c2b2f99b5e7b8cc61e6637d42eb8bd3cf21","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 few steps are made towards representation theory of embeddability among uncountable graphs. A monotone class of graphs is defined by forbidding countable subgraphs, related to the graph's end-structure. Using a combinatorial theorem of Shelah it is proved:\n - The complexity of the class in every regular uncountable $\\l>\\aleph_1$ is at least $\\lambda^+ + \\sup\\{\\mu^{\\aleph_0}:\\mu^+<\\lambda\\}$\n - For all regular uncountable $\\lambda>\\aleph_1$ there are $2^\\lambda$ pairwise non embeddable graphs in the class having strong homogeneity properties.\n - It is characterized when some invariants of a g","authors_text":"Menachem Kojman","cross_cats":[],"headline":"","license":"","primary_cat":"math.LO","submitted_at":"1995-07-24T00:00:00Z","title":"Representing embeddability as set inclusion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9507212","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":"sha256:64a7876994e7714834be3ab09313f71ad43b79815b3d5eccfde70350f63d13aa","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":"73cedb7915392db05f0d24d6e236c024087e82561d8cfc45d7d53b856642106c","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"1995-07-24T00:00:00Z","title_canon_sha256":"a9708ddecdc5e86eac98e764a69f9ea9f5002b372441bdfdc0f85c1cd8d3b7ab"},"schema_version":"1.0","source":{"id":"math/9507212","kind":"arxiv","version":1}},"canonical_sha256":"5c4c180c174ecab6393e94114e0d3d7d570e47f8b3ee15a7fad68db87be41203","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c4c180c174ecab6393e94114e0d3d7d570e47f8b3ee15a7fad68db87be41203","first_computed_at":"2026-05-18T01:05:48.503293Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:48.503293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"njTZnop+zEVPPX7KMZUZuEzxz6H0nrMDJ+Aebrh3vNhn10v5I7ZapiNUGQBPdI+B8JgBnqMAiXMQGdwtPUY9DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:48.503725Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9507212","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64a7876994e7714834be3ab09313f71ad43b79815b3d5eccfde70350f63d13aa","sha256:164a5778dbfa2664aa84cc35ea785c2b2f99b5e7b8cc61e6637d42eb8bd3cf21"],"state_sha256":"6b4539696e67e3ae2f9ac390b60d15565b3dd64f9740094809a8aa327610ce35"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iSvlsk6AqZL3vYPDJArQYcTZXvqdSUuk5qUDkDrcPZYpxyMpg5yvxYSd42XCjiSfD3YUKhrarjJgepkWJ5WjDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T17:03:47.224260Z","bundle_sha256":"582f9b994bfbfbac22d5ab36f981b8e6afce9eec30ca368fa9950f54258ca75e"}}