{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:D46IVHZ52XU7GTRP3Q4H7QP3VV","short_pith_number":"pith:D46IVHZ5","canonical_record":{"source":{"id":"2605.26199","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-05-25T17:12:46Z","cross_cats_sorted":["math.AT","math.CO"],"title_canon_sha256":"d0bd324ea326ac134da35558dcdc3562d4df5c0e4ec73291c09960fc3c1463f1","abstract_canon_sha256":"4aa83b98395d5ab78a1dbe238c647d8dae1ffdd8368981487fe00bf6bde74617"},"schema_version":"1.0"},"canonical_sha256":"1f3c8a9f3dd5e9f34e2fdc387fc1fbad54ccb8bd93cb6bf02cd79ffa5f61b223","source":{"kind":"arxiv","id":"2605.26199","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.26199","created_at":"2026-05-27T00:04:28Z"},{"alias_kind":"arxiv_version","alias_value":"2605.26199v1","created_at":"2026-05-27T00:04:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.26199","created_at":"2026-05-27T00:04:28Z"},{"alias_kind":"pith_short_12","alias_value":"D46IVHZ52XU7","created_at":"2026-05-27T00:04:28Z"},{"alias_kind":"pith_short_16","alias_value":"D46IVHZ52XU7GTRP","created_at":"2026-05-27T00:04:28Z"},{"alias_kind":"pith_short_8","alias_value":"D46IVHZ5","created_at":"2026-05-27T00:04:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:D46IVHZ52XU7GTRP3Q4H7QP3VV","target":"record","payload":{"canonical_record":{"source":{"id":"2605.26199","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-05-25T17:12:46Z","cross_cats_sorted":["math.AT","math.CO"],"title_canon_sha256":"d0bd324ea326ac134da35558dcdc3562d4df5c0e4ec73291c09960fc3c1463f1","abstract_canon_sha256":"4aa83b98395d5ab78a1dbe238c647d8dae1ffdd8368981487fe00bf6bde74617"},"schema_version":"1.0"},"canonical_sha256":"1f3c8a9f3dd5e9f34e2fdc387fc1fbad54ccb8bd93cb6bf02cd79ffa5f61b223","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T00:04:28.496114Z","signature_b64":"W/W5vnLesMBoh9oV1Lm8LEKFZUY32LXI2BmSntSL81F0vrfEn3prBjcvcgNjNbl46MG5YXoaqmapyj9FAudfAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f3c8a9f3dd5e9f34e2fdc387fc1fbad54ccb8bd93cb6bf02cd79ffa5f61b223","last_reissued_at":"2026-05-27T00:04:28.495385Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T00:04:28.495385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.26199","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":"2026-05-27T00:04:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3H3WXfPNY//jLES/p3TdBZDt0yoXTgG0LXfeV9fenKkEo3Ub0h7aUR267yAoyZslUnjEujFRVTTrlBc8BoVMDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T08:53:33.513542Z"},"content_sha256":"89df67b2aa7bb9e4a6a7c490943451e3c52f119cebb1026c0e943a7721cfb5d5","schema_version":"1.0","event_id":"sha256:89df67b2aa7bb9e4a6a7c490943451e3c52f119cebb1026c0e943a7721cfb5d5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:D46IVHZ52XU7GTRP3Q4H7QP3VV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On partial groups of small order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CO"],"primary_cat":"math.GR","authors_text":"Philip Hackney","submitted_at":"2026-05-25T17:12:46Z","abstract_excerpt":"There are 123,650 partial groups of order at most 9 and 178,937,003 partial groups of order 10. We explain a computer enumeration of these results and provide a complete list of indecomposable partial groups of order at most 5. We also indicate results that were discovered through computational experiments."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26199","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/2605.26199/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":"2026-05-27T00:04:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L2XXWXv1tfcIZ8nMyAEh+OAtgW2Dhtf5tR+8L4KmJZWMXHdaaWFJARUIuP11BS3RgamSFDQc4lnGnXMlfyipCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T08:53:33.514207Z"},"content_sha256":"4fb06d53a8f7f70d144d8a4b45a1dd82398044f72f32fe38bb69d18a5ccdf6a8","schema_version":"1.0","event_id":"sha256:4fb06d53a8f7f70d144d8a4b45a1dd82398044f72f32fe38bb69d18a5ccdf6a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D46IVHZ52XU7GTRP3Q4H7QP3VV/bundle.json","state_url":"https://pith.science/pith/D46IVHZ52XU7GTRP3Q4H7QP3VV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D46IVHZ52XU7GTRP3Q4H7QP3VV/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":"2026-06-04T08:53:33Z","links":{"resolver":"https://pith.science/pith/D46IVHZ52XU7GTRP3Q4H7QP3VV","bundle":"https://pith.science/pith/D46IVHZ52XU7GTRP3Q4H7QP3VV/bundle.json","state":"https://pith.science/pith/D46IVHZ52XU7GTRP3Q4H7QP3VV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D46IVHZ52XU7GTRP3Q4H7QP3VV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:D46IVHZ52XU7GTRP3Q4H7QP3VV","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":"4aa83b98395d5ab78a1dbe238c647d8dae1ffdd8368981487fe00bf6bde74617","cross_cats_sorted":["math.AT","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-05-25T17:12:46Z","title_canon_sha256":"d0bd324ea326ac134da35558dcdc3562d4df5c0e4ec73291c09960fc3c1463f1"},"schema_version":"1.0","source":{"id":"2605.26199","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.26199","created_at":"2026-05-27T00:04:28Z"},{"alias_kind":"arxiv_version","alias_value":"2605.26199v1","created_at":"2026-05-27T00:04:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.26199","created_at":"2026-05-27T00:04:28Z"},{"alias_kind":"pith_short_12","alias_value":"D46IVHZ52XU7","created_at":"2026-05-27T00:04:28Z"},{"alias_kind":"pith_short_16","alias_value":"D46IVHZ52XU7GTRP","created_at":"2026-05-27T00:04:28Z"},{"alias_kind":"pith_short_8","alias_value":"D46IVHZ5","created_at":"2026-05-27T00:04:28Z"}],"graph_snapshots":[{"event_id":"sha256:4fb06d53a8f7f70d144d8a4b45a1dd82398044f72f32fe38bb69d18a5ccdf6a8","target":"graph","created_at":"2026-05-27T00:04:28Z","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/2605.26199/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"There are 123,650 partial groups of order at most 9 and 178,937,003 partial groups of order 10. We explain a computer enumeration of these results and provide a complete list of indecomposable partial groups of order at most 5. We also indicate results that were discovered through computational experiments.","authors_text":"Philip Hackney","cross_cats":["math.AT","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-05-25T17:12:46Z","title":"On partial groups of small order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26199","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":"sha256:89df67b2aa7bb9e4a6a7c490943451e3c52f119cebb1026c0e943a7721cfb5d5","target":"record","created_at":"2026-05-27T00:04:28Z","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":"4aa83b98395d5ab78a1dbe238c647d8dae1ffdd8368981487fe00bf6bde74617","cross_cats_sorted":["math.AT","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-05-25T17:12:46Z","title_canon_sha256":"d0bd324ea326ac134da35558dcdc3562d4df5c0e4ec73291c09960fc3c1463f1"},"schema_version":"1.0","source":{"id":"2605.26199","kind":"arxiv","version":1}},"canonical_sha256":"1f3c8a9f3dd5e9f34e2fdc387fc1fbad54ccb8bd93cb6bf02cd79ffa5f61b223","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f3c8a9f3dd5e9f34e2fdc387fc1fbad54ccb8bd93cb6bf02cd79ffa5f61b223","first_computed_at":"2026-05-27T00:04:28.495385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T00:04:28.495385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W/W5vnLesMBoh9oV1Lm8LEKFZUY32LXI2BmSntSL81F0vrfEn3prBjcvcgNjNbl46MG5YXoaqmapyj9FAudfAw==","signature_status":"signed_v1","signed_at":"2026-05-27T00:04:28.496114Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.26199","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89df67b2aa7bb9e4a6a7c490943451e3c52f119cebb1026c0e943a7721cfb5d5","sha256:4fb06d53a8f7f70d144d8a4b45a1dd82398044f72f32fe38bb69d18a5ccdf6a8"],"state_sha256":"db2d5d9d0b5af7f59f858ec331b33492ef3beb43fbda4423dc2ad1ec14c7c93a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PpGg2n6U26m/abp9mTcKwXCga/vPcTRL5wnUCsNWkfx7oBLa2FnlSSw0fe6cnIS4Vke56pZQ3bCpumTUPPwdAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T08:53:33.517845Z","bundle_sha256":"06b97b21ad8a4bf7816fbc31ea05c263b65a376c9040bf54111d0c5c429f6d70"}}