{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:7I3XV7GD2J6KAK2VT625P3MOQA","short_pith_number":"pith:7I3XV7GD","canonical_record":{"source":{"id":"1509.07674","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-09-25T11:02:44Z","cross_cats_sorted":["math.CO","math.GR"],"title_canon_sha256":"27a7ec9e1ac609065e2fe02804bbc56062b5f6680fb77ef3eec132ddbce78bb8","abstract_canon_sha256":"6923239a2f665f91be02ac9b90e819c0977b269bdb4a565bf96af86a55b28935"},"schema_version":"1.0"},"canonical_sha256":"fa377afcc3d27ca02b559fb5d7ed8e800a7f6ff17edea33ba4795c558a71b074","source":{"kind":"arxiv","id":"1509.07674","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07674","created_at":"2026-05-18T01:32:02Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07674v1","created_at":"2026-05-18T01:32:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07674","created_at":"2026-05-18T01:32:02Z"},{"alias_kind":"pith_short_12","alias_value":"7I3XV7GD2J6K","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7I3XV7GD2J6KAK2V","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7I3XV7GD","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:7I3XV7GD2J6KAK2VT625P3MOQA","target":"record","payload":{"canonical_record":{"source":{"id":"1509.07674","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-09-25T11:02:44Z","cross_cats_sorted":["math.CO","math.GR"],"title_canon_sha256":"27a7ec9e1ac609065e2fe02804bbc56062b5f6680fb77ef3eec132ddbce78bb8","abstract_canon_sha256":"6923239a2f665f91be02ac9b90e819c0977b269bdb4a565bf96af86a55b28935"},"schema_version":"1.0"},"canonical_sha256":"fa377afcc3d27ca02b559fb5d7ed8e800a7f6ff17edea33ba4795c558a71b074","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:02.213200Z","signature_b64":"No44MDYeQGlPWkt7cSMctS8BvzxVgn9I48+dk1IIJ+NdJKgCQSxuwxEXXWx0RrbbWh3g5G4iJ+I8YarerpzPDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa377afcc3d27ca02b559fb5d7ed8e800a7f6ff17edea33ba4795c558a71b074","last_reissued_at":"2026-05-18T01:32:02.212776Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:02.212776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.07674","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":"2026-05-18T01:32:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V9LBqFk9bolLQZyRhJHvzNyAo56lufaddma+7zMh7EwDLOSdXriDfO09xU67EMllz/ncTc2ZunhNoTSC+vRqDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:20:12.667793Z"},"content_sha256":"d03b70b03ed2a6392785e36229eda27c30a9e4e8adc1b3f49b3c672166c056cd","schema_version":"1.0","event_id":"sha256:d03b70b03ed2a6392785e36229eda27c30a9e4e8adc1b3f49b3c672166c056cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:7I3XV7GD2J6KAK2VT625P3MOQA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$2^{\\aleph_0}$ pairwise non-isomorphic maximal-closed subgroups of Sym$(\\mathbb{N})$ via the classification of the reducts of the Henson digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GR"],"primary_cat":"math.LO","authors_text":"Lovkush Agarwal, Michael Kompatscher","submitted_at":"2015-09-25T11:02:44Z","abstract_excerpt":"Given two structures $\\mathcal{M}$ and $\\mathcal{N}$ on the same domain, we say that $\\mathcal{N}$ is a reduct of $\\mathcal{M}$ if all $\\emptyset$-definable relations of $\\mathcal{N}$ are $\\emptyset$-definable in $\\mathcal{M}$. In this article the reducts of the Henson digraphs are classified. Henson digraphs are homogeneous countable digraphs that omit some set of finite tournaments. As the Henson digraphs are $\\aleph_0$-categorical, determining their reducts is equivalent to determining all closed supergroups $G<$ Sym$(\\mathbb{N})$ of their automorphism groups.\n  A consequence of the classif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07674","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":"2026-05-18T01:32:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kVKEv30U9iLcw5PiJv5ZatL2lYPg4eCyDhPcZv88mMiSEwZUkXEgn3iS7tMXAY/wa22oHBufToKyXO0hBYlICg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:20:12.668136Z"},"content_sha256":"1dd092e83e5194a8b93815b6c6d7cfe6d7f9f8d8e6f0d7660f879399c671f3e3","schema_version":"1.0","event_id":"sha256:1dd092e83e5194a8b93815b6c6d7cfe6d7f9f8d8e6f0d7660f879399c671f3e3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7I3XV7GD2J6KAK2VT625P3MOQA/bundle.json","state_url":"https://pith.science/pith/7I3XV7GD2J6KAK2VT625P3MOQA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7I3XV7GD2J6KAK2VT625P3MOQA/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":"2026-06-09T10:20:12Z","links":{"resolver":"https://pith.science/pith/7I3XV7GD2J6KAK2VT625P3MOQA","bundle":"https://pith.science/pith/7I3XV7GD2J6KAK2VT625P3MOQA/bundle.json","state":"https://pith.science/pith/7I3XV7GD2J6KAK2VT625P3MOQA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7I3XV7GD2J6KAK2VT625P3MOQA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7I3XV7GD2J6KAK2VT625P3MOQA","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":"6923239a2f665f91be02ac9b90e819c0977b269bdb4a565bf96af86a55b28935","cross_cats_sorted":["math.CO","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-09-25T11:02:44Z","title_canon_sha256":"27a7ec9e1ac609065e2fe02804bbc56062b5f6680fb77ef3eec132ddbce78bb8"},"schema_version":"1.0","source":{"id":"1509.07674","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07674","created_at":"2026-05-18T01:32:02Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07674v1","created_at":"2026-05-18T01:32:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07674","created_at":"2026-05-18T01:32:02Z"},{"alias_kind":"pith_short_12","alias_value":"7I3XV7GD2J6K","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7I3XV7GD2J6KAK2V","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7I3XV7GD","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:1dd092e83e5194a8b93815b6c6d7cfe6d7f9f8d8e6f0d7660f879399c671f3e3","target":"graph","created_at":"2026-05-18T01:32:02Z","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":"Given two structures $\\mathcal{M}$ and $\\mathcal{N}$ on the same domain, we say that $\\mathcal{N}$ is a reduct of $\\mathcal{M}$ if all $\\emptyset$-definable relations of $\\mathcal{N}$ are $\\emptyset$-definable in $\\mathcal{M}$. In this article the reducts of the Henson digraphs are classified. Henson digraphs are homogeneous countable digraphs that omit some set of finite tournaments. As the Henson digraphs are $\\aleph_0$-categorical, determining their reducts is equivalent to determining all closed supergroups $G<$ Sym$(\\mathbb{N})$ of their automorphism groups.\n  A consequence of the classif","authors_text":"Lovkush Agarwal, Michael Kompatscher","cross_cats":["math.CO","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-09-25T11:02:44Z","title":"$2^{\\aleph_0}$ pairwise non-isomorphic maximal-closed subgroups of Sym$(\\mathbb{N})$ via the classification of the reducts of the Henson digraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07674","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:d03b70b03ed2a6392785e36229eda27c30a9e4e8adc1b3f49b3c672166c056cd","target":"record","created_at":"2026-05-18T01:32:02Z","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":"6923239a2f665f91be02ac9b90e819c0977b269bdb4a565bf96af86a55b28935","cross_cats_sorted":["math.CO","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-09-25T11:02:44Z","title_canon_sha256":"27a7ec9e1ac609065e2fe02804bbc56062b5f6680fb77ef3eec132ddbce78bb8"},"schema_version":"1.0","source":{"id":"1509.07674","kind":"arxiv","version":1}},"canonical_sha256":"fa377afcc3d27ca02b559fb5d7ed8e800a7f6ff17edea33ba4795c558a71b074","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa377afcc3d27ca02b559fb5d7ed8e800a7f6ff17edea33ba4795c558a71b074","first_computed_at":"2026-05-18T01:32:02.212776Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:02.212776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"No44MDYeQGlPWkt7cSMctS8BvzxVgn9I48+dk1IIJ+NdJKgCQSxuwxEXXWx0RrbbWh3g5G4iJ+I8YarerpzPDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:02.213200Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.07674","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d03b70b03ed2a6392785e36229eda27c30a9e4e8adc1b3f49b3c672166c056cd","sha256:1dd092e83e5194a8b93815b6c6d7cfe6d7f9f8d8e6f0d7660f879399c671f3e3"],"state_sha256":"b66e41471595471469b9d70b64576163e00334ef0545a299c199851f037f6a49"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W1E2czhnBhD8+oEcRQbyjRMjee84XgmpIjXbP2QoOvRkzCaWjSuW91GGcbjS3gH1EwZgzBVzQ4rsc9tItQr3DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T10:20:12.669974Z","bundle_sha256":"cac9c2d468ac61313530e531af716f564efe061cd5fcddc973c2e2d8b70abc4e"}}