{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:4SK7SUU4CK6GSWLDO67NAPONP7","short_pith_number":"pith:4SK7SUU4","canonical_record":{"source":{"id":"2507.05471","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2025-07-07T20:45:42Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"831dc887f39c12011a8603f8970e8fb3bdeddb605a320f77b45c7a3b4899925c","abstract_canon_sha256":"cf5b7dafb3a72243e2dabc4e65e8213325dff7e590de3a544730e821068fc376"},"schema_version":"1.0"},"canonical_sha256":"e495f9529c12bc69596377bed03dcd7fd82aee3f10a479ee3f030aebb4d2a7e3","source":{"kind":"arxiv","id":"2507.05471","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.05471","created_at":"2026-07-05T11:33:31Z"},{"alias_kind":"arxiv_version","alias_value":"2507.05471v1","created_at":"2026-07-05T11:33:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.05471","created_at":"2026-07-05T11:33:31Z"},{"alias_kind":"pith_short_12","alias_value":"4SK7SUU4CK6G","created_at":"2026-07-05T11:33:31Z"},{"alias_kind":"pith_short_16","alias_value":"4SK7SUU4CK6GSWLD","created_at":"2026-07-05T11:33:31Z"},{"alias_kind":"pith_short_8","alias_value":"4SK7SUU4","created_at":"2026-07-05T11:33:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:4SK7SUU4CK6GSWLDO67NAPONP7","target":"record","payload":{"canonical_record":{"source":{"id":"2507.05471","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2025-07-07T20:45:42Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"831dc887f39c12011a8603f8970e8fb3bdeddb605a320f77b45c7a3b4899925c","abstract_canon_sha256":"cf5b7dafb3a72243e2dabc4e65e8213325dff7e590de3a544730e821068fc376"},"schema_version":"1.0"},"canonical_sha256":"e495f9529c12bc69596377bed03dcd7fd82aee3f10a479ee3f030aebb4d2a7e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:33:31.087868Z","signature_b64":"TZ4kvC+8+jpGL2NcywapslU7bC5hx3ZVu8874JGiFi/iVUdCneD5P0sZq/wvjve1pGNqAgx9xqx518whzIMJAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e495f9529c12bc69596377bed03dcd7fd82aee3f10a479ee3f030aebb4d2a7e3","last_reissued_at":"2026-07-05T11:33:31.087474Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:33:31.087474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.05471","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":"2026-07-05T11:33:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E9noS4d2csiM8ROOYBraozm9LUHq3zA6w2RhBdafsR37M0AAvRfSdIpVzub3hOb42C3GVJAXo8Ph0ljvIFRIBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T09:59:55.548476Z"},"content_sha256":"bcb994279ea0c0b01bf028402d8183b5fef551bc33fbb87afa9fb4789eda5bc8","schema_version":"1.0","event_id":"sha256:bcb994279ea0c0b01bf028402d8183b5fef551bc33fbb87afa9fb4789eda5bc8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:4SK7SUU4CK6GSWLDO67NAPONP7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher limits of wider systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.LO","authors_text":"Jeffrey Bergfalk, Matteo Casarosa","submitted_at":"2025-07-07T20:45:42Z","abstract_excerpt":"Write $\\mathbf{A}_\\lambda$ for what might be described as the most elementary nontrivial inverse system of abelian groups indexed by the functions from the cardinal $\\lambda$ to the set of natural numbers. The question of whether for any fixed $n$ the derived limit $\\mathrm{lim}^n\\,\\mathbf{A}_\\lambda$ may vanish for only a nonempty subset of the class of infinite cardinals $\\lambda$ is recorded in both [Be17] and [Ban23], and bears closely on several related further ones. We answer this question in the affirmative; in fact, we show the maximal possibility, namely that this can simultaneously h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.05471","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/2507.05471/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":"2026-07-05T11:33:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"szN6u99WEo17KbveOGZMGOgzOsGQgd+VEJwO981w6yCb57tyfzP0KV7jfOhjpTbtzk/aTAa8VUccCUHzaHZsDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T09:59:55.549000Z"},"content_sha256":"2f83b545ceb3498ffd362b20701698f08a70dabc6306a19cbb5252b92ddea284","schema_version":"1.0","event_id":"sha256:2f83b545ceb3498ffd362b20701698f08a70dabc6306a19cbb5252b92ddea284"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4SK7SUU4CK6GSWLDO67NAPONP7/bundle.json","state_url":"https://pith.science/pith/4SK7SUU4CK6GSWLDO67NAPONP7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4SK7SUU4CK6GSWLDO67NAPONP7/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":"2026-08-12T09:59:55Z","links":{"resolver":"https://pith.science/pith/4SK7SUU4CK6GSWLDO67NAPONP7","bundle":"https://pith.science/pith/4SK7SUU4CK6GSWLDO67NAPONP7/bundle.json","state":"https://pith.science/pith/4SK7SUU4CK6GSWLDO67NAPONP7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4SK7SUU4CK6GSWLDO67NAPONP7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:4SK7SUU4CK6GSWLDO67NAPONP7","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":"cf5b7dafb3a72243e2dabc4e65e8213325dff7e590de3a544730e821068fc376","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2025-07-07T20:45:42Z","title_canon_sha256":"831dc887f39c12011a8603f8970e8fb3bdeddb605a320f77b45c7a3b4899925c"},"schema_version":"1.0","source":{"id":"2507.05471","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.05471","created_at":"2026-07-05T11:33:31Z"},{"alias_kind":"arxiv_version","alias_value":"2507.05471v1","created_at":"2026-07-05T11:33:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.05471","created_at":"2026-07-05T11:33:31Z"},{"alias_kind":"pith_short_12","alias_value":"4SK7SUU4CK6G","created_at":"2026-07-05T11:33:31Z"},{"alias_kind":"pith_short_16","alias_value":"4SK7SUU4CK6GSWLD","created_at":"2026-07-05T11:33:31Z"},{"alias_kind":"pith_short_8","alias_value":"4SK7SUU4","created_at":"2026-07-05T11:33:31Z"}],"graph_snapshots":[{"event_id":"sha256:2f83b545ceb3498ffd362b20701698f08a70dabc6306a19cbb5252b92ddea284","target":"graph","created_at":"2026-07-05T11:33:31Z","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/2507.05471/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Write $\\mathbf{A}_\\lambda$ for what might be described as the most elementary nontrivial inverse system of abelian groups indexed by the functions from the cardinal $\\lambda$ to the set of natural numbers. The question of whether for any fixed $n$ the derived limit $\\mathrm{lim}^n\\,\\mathbf{A}_\\lambda$ may vanish for only a nonempty subset of the class of infinite cardinals $\\lambda$ is recorded in both [Be17] and [Ban23], and bears closely on several related further ones. We answer this question in the affirmative; in fact, we show the maximal possibility, namely that this can simultaneously h","authors_text":"Jeffrey Bergfalk, Matteo Casarosa","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2025-07-07T20:45:42Z","title":"Higher limits of wider systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.05471","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:bcb994279ea0c0b01bf028402d8183b5fef551bc33fbb87afa9fb4789eda5bc8","target":"record","created_at":"2026-07-05T11:33:31Z","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":"cf5b7dafb3a72243e2dabc4e65e8213325dff7e590de3a544730e821068fc376","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2025-07-07T20:45:42Z","title_canon_sha256":"831dc887f39c12011a8603f8970e8fb3bdeddb605a320f77b45c7a3b4899925c"},"schema_version":"1.0","source":{"id":"2507.05471","kind":"arxiv","version":1}},"canonical_sha256":"e495f9529c12bc69596377bed03dcd7fd82aee3f10a479ee3f030aebb4d2a7e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e495f9529c12bc69596377bed03dcd7fd82aee3f10a479ee3f030aebb4d2a7e3","first_computed_at":"2026-07-05T11:33:31.087474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:33:31.087474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TZ4kvC+8+jpGL2NcywapslU7bC5hx3ZVu8874JGiFi/iVUdCneD5P0sZq/wvjve1pGNqAgx9xqx518whzIMJAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:33:31.087868Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.05471","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bcb994279ea0c0b01bf028402d8183b5fef551bc33fbb87afa9fb4789eda5bc8","sha256:2f83b545ceb3498ffd362b20701698f08a70dabc6306a19cbb5252b92ddea284"],"state_sha256":"6e21a704e1f7be0df507f7d38c4165900d8da6f8e5898a720eccca340cf68d1d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sx8jec4UKWjv5qefUjL4DpH4bZIVIyYqDljIjOSmKV3TsFJqoXh04DIlmebzTkeABBdzRaasqgYL2tlKNEzICw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T09:59:55.552641Z","bundle_sha256":"b2392ddb9d6ff899bc245d1e8ae8780b0094488d237b9906da1183e01ab4707a"}}