{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:CNXKNITO3GTSNCFNLGL2CNO36A","short_pith_number":"pith:CNXKNITO","canonical_record":{"source":{"id":"2501.03768","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.GR","submitted_at":"2025-01-07T13:21:16Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"3d02e8cfbbe222a0fb833727b4482fa36de953cca7ae9bbf15b699a6f5a07798","abstract_canon_sha256":"883c01a91ca8ae8bfe163db63207baaaf2bc187c4c579a9a5155ecc6d9b1f748"},"schema_version":"1.0"},"canonical_sha256":"136ea6a26ed9a72688ad5997a135dbf001955622b603577a8088804dda99e1c2","source":{"kind":"arxiv","id":"2501.03768","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.03768","created_at":"2026-05-26T02:04:59Z"},{"alias_kind":"arxiv_version","alias_value":"2501.03768v1","created_at":"2026-05-26T02:04:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.03768","created_at":"2026-05-26T02:04:59Z"},{"alias_kind":"pith_short_12","alias_value":"CNXKNITO3GTS","created_at":"2026-05-26T02:04:59Z"},{"alias_kind":"pith_short_16","alias_value":"CNXKNITO3GTSNCFN","created_at":"2026-05-26T02:04:59Z"},{"alias_kind":"pith_short_8","alias_value":"CNXKNITO","created_at":"2026-05-26T02:04:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:CNXKNITO3GTSNCFNLGL2CNO36A","target":"record","payload":{"canonical_record":{"source":{"id":"2501.03768","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.GR","submitted_at":"2025-01-07T13:21:16Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"3d02e8cfbbe222a0fb833727b4482fa36de953cca7ae9bbf15b699a6f5a07798","abstract_canon_sha256":"883c01a91ca8ae8bfe163db63207baaaf2bc187c4c579a9a5155ecc6d9b1f748"},"schema_version":"1.0"},"canonical_sha256":"136ea6a26ed9a72688ad5997a135dbf001955622b603577a8088804dda99e1c2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:04:59.430727Z","signature_b64":"t0zU8IVKzuRtABK/rESMjnbmGkQKnH5bPbZlbvB7tFQhn0OKsmeyoE5nkRSKDiDn1Y7sQheeHcOJXi8DLoaLCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"136ea6a26ed9a72688ad5997a135dbf001955622b603577a8088804dda99e1c2","last_reissued_at":"2026-05-26T02:04:59.430054Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:04:59.430054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.03768","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":"2026-05-26T02:04:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zxdTUYmCRZdl6UzAFjoxT+VI4mZ8ev0Zzij5ApDaeo2pUtHYrD3Q5mJMLMxpdSLcHaGaaherFsr4fFW0ErIoCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:30:28.876644Z"},"content_sha256":"a10f0995a7160cc83b7d3ee6056591f7f92816c70c9b19293b3f66de7a8301ee","schema_version":"1.0","event_id":"sha256:a10f0995a7160cc83b7d3ee6056591f7f92816c70c9b19293b3f66de7a8301ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:CNXKNITO3GTSNCFNLGL2CNO36A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"When Max_d(G) is zero-dimensional","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.GR","authors_text":"Ramiro Lafuente-Rodriguez, Ricardo Carrera, Warren Wm. McGovern","submitted_at":"2025-01-07T13:21:16Z","abstract_excerpt":"This article is a continuation of [6] where a classification of when the space of minimal prime subgroups of a given lattice-ordered group equipped with the inverse topology has a clopen $\\pi$-base. For nice $\\ell$-groups, (e.g. W-objects) this occurs precisely when the space of maximal $d$-subgroups (qua the hull kernel topology) has a clopen $\\pi$-base. It occurred to us that presently there is no classification of when the space of maximal $d$-subgroups of a W-object is zero-dimensional, except for the case of the $C(X)$, the real-valued continuous functions on a topological space $X$, cons"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.03768","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/2501.03768/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":"2026-05-26T02:04:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nc543g3EZ230j4SLsClUpKHMv/z3HeBDV5sc2tmeV2EVJ1CNccCS77mRssQcoFrI4fxVdIfTErgYJTnSeG1PDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:30:28.877024Z"},"content_sha256":"a31ee7770fcd3aee59961c2d2ea50c6688e76175809278d91b116783adf83960","schema_version":"1.0","event_id":"sha256:a31ee7770fcd3aee59961c2d2ea50c6688e76175809278d91b116783adf83960"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CNXKNITO3GTSNCFNLGL2CNO36A/bundle.json","state_url":"https://pith.science/pith/CNXKNITO3GTSNCFNLGL2CNO36A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CNXKNITO3GTSNCFNLGL2CNO36A/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":"2026-06-02T12:30:28Z","links":{"resolver":"https://pith.science/pith/CNXKNITO3GTSNCFNLGL2CNO36A","bundle":"https://pith.science/pith/CNXKNITO3GTSNCFNLGL2CNO36A/bundle.json","state":"https://pith.science/pith/CNXKNITO3GTSNCFNLGL2CNO36A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CNXKNITO3GTSNCFNLGL2CNO36A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:CNXKNITO3GTSNCFNLGL2CNO36A","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":"883c01a91ca8ae8bfe163db63207baaaf2bc187c4c579a9a5155ecc6d9b1f748","cross_cats_sorted":["math.GN"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.GR","submitted_at":"2025-01-07T13:21:16Z","title_canon_sha256":"3d02e8cfbbe222a0fb833727b4482fa36de953cca7ae9bbf15b699a6f5a07798"},"schema_version":"1.0","source":{"id":"2501.03768","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.03768","created_at":"2026-05-26T02:04:59Z"},{"alias_kind":"arxiv_version","alias_value":"2501.03768v1","created_at":"2026-05-26T02:04:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.03768","created_at":"2026-05-26T02:04:59Z"},{"alias_kind":"pith_short_12","alias_value":"CNXKNITO3GTS","created_at":"2026-05-26T02:04:59Z"},{"alias_kind":"pith_short_16","alias_value":"CNXKNITO3GTSNCFN","created_at":"2026-05-26T02:04:59Z"},{"alias_kind":"pith_short_8","alias_value":"CNXKNITO","created_at":"2026-05-26T02:04:59Z"}],"graph_snapshots":[{"event_id":"sha256:a31ee7770fcd3aee59961c2d2ea50c6688e76175809278d91b116783adf83960","target":"graph","created_at":"2026-05-26T02:04:59Z","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/2501.03768/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This article is a continuation of [6] where a classification of when the space of minimal prime subgroups of a given lattice-ordered group equipped with the inverse topology has a clopen $\\pi$-base. For nice $\\ell$-groups, (e.g. W-objects) this occurs precisely when the space of maximal $d$-subgroups (qua the hull kernel topology) has a clopen $\\pi$-base. It occurred to us that presently there is no classification of when the space of maximal $d$-subgroups of a W-object is zero-dimensional, except for the case of the $C(X)$, the real-valued continuous functions on a topological space $X$, cons","authors_text":"Ramiro Lafuente-Rodriguez, Ricardo Carrera, Warren Wm. McGovern","cross_cats":["math.GN"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.GR","submitted_at":"2025-01-07T13:21:16Z","title":"When Max_d(G) is zero-dimensional"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.03768","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:a10f0995a7160cc83b7d3ee6056591f7f92816c70c9b19293b3f66de7a8301ee","target":"record","created_at":"2026-05-26T02:04:59Z","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":"883c01a91ca8ae8bfe163db63207baaaf2bc187c4c579a9a5155ecc6d9b1f748","cross_cats_sorted":["math.GN"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.GR","submitted_at":"2025-01-07T13:21:16Z","title_canon_sha256":"3d02e8cfbbe222a0fb833727b4482fa36de953cca7ae9bbf15b699a6f5a07798"},"schema_version":"1.0","source":{"id":"2501.03768","kind":"arxiv","version":1}},"canonical_sha256":"136ea6a26ed9a72688ad5997a135dbf001955622b603577a8088804dda99e1c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"136ea6a26ed9a72688ad5997a135dbf001955622b603577a8088804dda99e1c2","first_computed_at":"2026-05-26T02:04:59.430054Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T02:04:59.430054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t0zU8IVKzuRtABK/rESMjnbmGkQKnH5bPbZlbvB7tFQhn0OKsmeyoE5nkRSKDiDn1Y7sQheeHcOJXi8DLoaLCA==","signature_status":"signed_v1","signed_at":"2026-05-26T02:04:59.430727Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.03768","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a10f0995a7160cc83b7d3ee6056591f7f92816c70c9b19293b3f66de7a8301ee","sha256:a31ee7770fcd3aee59961c2d2ea50c6688e76175809278d91b116783adf83960"],"state_sha256":"275360499dd7840f0695221151a4865b5c3d1b5dcefbe18035b0d8d71e310217"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0pcykBB/tuB1YwzN1UGr4LX523/gBP10hOFUqMgGdI5K9k83A31DV2/LlchUT/YQAVb43FgMlzRUppNhkAwfBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T12:30:28.879254Z","bundle_sha256":"194bc8e5ba0bbcb629beb484e5d13200f63ed392a24524201fb456188dd81715"}}