{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:4BDLSEVO3TML74RTUTMEDELYCM","short_pith_number":"pith:4BDLSEVO","canonical_record":{"source":{"id":"1402.4825","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-19T21:05:40Z","cross_cats_sorted":[],"title_canon_sha256":"584b4557423c8fc9b447724de7d8fb45bf345acd52958d0dc4861af68dd8ba7d","abstract_canon_sha256":"189105c0fff9b08f69f74d470df45fd061bf71d42dc11af36300475fda7d3c03"},"schema_version":"1.0"},"canonical_sha256":"e046b912aedcd8bff233a4d8419178130943f89a606312bc9e9e02970206bfa5","source":{"kind":"arxiv","id":"1402.4825","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.4825","created_at":"2026-05-18T02:58:32Z"},{"alias_kind":"arxiv_version","alias_value":"1402.4825v1","created_at":"2026-05-18T02:58:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.4825","created_at":"2026-05-18T02:58:32Z"},{"alias_kind":"pith_short_12","alias_value":"4BDLSEVO3TML","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4BDLSEVO3TML74RT","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4BDLSEVO","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:4BDLSEVO3TML74RTUTMEDELYCM","target":"record","payload":{"canonical_record":{"source":{"id":"1402.4825","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-19T21:05:40Z","cross_cats_sorted":[],"title_canon_sha256":"584b4557423c8fc9b447724de7d8fb45bf345acd52958d0dc4861af68dd8ba7d","abstract_canon_sha256":"189105c0fff9b08f69f74d470df45fd061bf71d42dc11af36300475fda7d3c03"},"schema_version":"1.0"},"canonical_sha256":"e046b912aedcd8bff233a4d8419178130943f89a606312bc9e9e02970206bfa5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:32.042794Z","signature_b64":"NkGvmi+VzAAIu6c6MGTdtI1cVjfjEk9v1rtCP327XDu/Ug9gMUZyPv7o0j3DWwVnmnguoq7TRvCfY7+vZlMtAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e046b912aedcd8bff233a4d8419178130943f89a606312bc9e9e02970206bfa5","last_reissued_at":"2026-05-18T02:58:32.042251Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:32.042251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.4825","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":"2026-05-18T02:58:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OKgMpwbrJs67ipNrptB8bfK+6TI83CZts+6XdjHgeJ/vhNj9i7hE9H5/9a6XR48B/vgoBCuKu25x0ndZyHmdAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T15:23:57.995843Z"},"content_sha256":"691faa2c36cc59ceee6ebb37f9146d0aa4c7b2e87cce80af9485a77df5fb724b","schema_version":"1.0","event_id":"sha256:691faa2c36cc59ceee6ebb37f9146d0aa4c7b2e87cce80af9485a77df5fb724b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:4BDLSEVO3TML74RTUTMEDELYCM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Bass and topological stable ranks for algebras of almost periodic functions on the real line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Raymond Mortini, Rudolf Rupp","submitted_at":"2014-02-19T21:05:40Z","abstract_excerpt":"Let $\\Lambda$ be a sub-semigroup of the reals. We show that the Bass and topological stable ranks of the algebras ${\\rm AP}_\\Lambda=\\{f\\in {\\rm AP}: \\sigma(f)\\subseteq \\Lambda\\}$ of almost periodic functions on the real line and with Bohr spectrum in $\\Lambda$ are infinite whenever the algebraic dimension of the $\\mathbb Q$-vector space generated by $\\Lambda$ is infinite. This extends Su\\'arez's result for ${\\rm AP}_\\mathbb R={\\rm AP}$. Also considered are general subalgebras of AP."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4825","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":"2026-05-18T02:58:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mgns8G3hkaccnI4UV4Lxa5KTqYXDGFo/iAKtC+h1DlZuW7UubQ46xsZ+kIs8kMPgbPI0pEuvu0nrschIf7LiBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T15:23:57.996188Z"},"content_sha256":"535a6b01c21c228276a927553a2d83fead08b2822db462d2af460e6b6c5c63d0","schema_version":"1.0","event_id":"sha256:535a6b01c21c228276a927553a2d83fead08b2822db462d2af460e6b6c5c63d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4BDLSEVO3TML74RTUTMEDELYCM/bundle.json","state_url":"https://pith.science/pith/4BDLSEVO3TML74RTUTMEDELYCM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4BDLSEVO3TML74RTUTMEDELYCM/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":"2026-07-02T15:23:57Z","links":{"resolver":"https://pith.science/pith/4BDLSEVO3TML74RTUTMEDELYCM","bundle":"https://pith.science/pith/4BDLSEVO3TML74RTUTMEDELYCM/bundle.json","state":"https://pith.science/pith/4BDLSEVO3TML74RTUTMEDELYCM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4BDLSEVO3TML74RTUTMEDELYCM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4BDLSEVO3TML74RTUTMEDELYCM","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":"189105c0fff9b08f69f74d470df45fd061bf71d42dc11af36300475fda7d3c03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-19T21:05:40Z","title_canon_sha256":"584b4557423c8fc9b447724de7d8fb45bf345acd52958d0dc4861af68dd8ba7d"},"schema_version":"1.0","source":{"id":"1402.4825","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.4825","created_at":"2026-05-18T02:58:32Z"},{"alias_kind":"arxiv_version","alias_value":"1402.4825v1","created_at":"2026-05-18T02:58:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.4825","created_at":"2026-05-18T02:58:32Z"},{"alias_kind":"pith_short_12","alias_value":"4BDLSEVO3TML","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4BDLSEVO3TML74RT","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4BDLSEVO","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:535a6b01c21c228276a927553a2d83fead08b2822db462d2af460e6b6c5c63d0","target":"graph","created_at":"2026-05-18T02:58:32Z","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":"Let $\\Lambda$ be a sub-semigroup of the reals. We show that the Bass and topological stable ranks of the algebras ${\\rm AP}_\\Lambda=\\{f\\in {\\rm AP}: \\sigma(f)\\subseteq \\Lambda\\}$ of almost periodic functions on the real line and with Bohr spectrum in $\\Lambda$ are infinite whenever the algebraic dimension of the $\\mathbb Q$-vector space generated by $\\Lambda$ is infinite. This extends Su\\'arez's result for ${\\rm AP}_\\mathbb R={\\rm AP}$. Also considered are general subalgebras of AP.","authors_text":"Raymond Mortini, Rudolf Rupp","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-19T21:05:40Z","title":"The Bass and topological stable ranks for algebras of almost periodic functions on the real line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4825","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":"sha256:691faa2c36cc59ceee6ebb37f9146d0aa4c7b2e87cce80af9485a77df5fb724b","target":"record","created_at":"2026-05-18T02:58:32Z","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":"189105c0fff9b08f69f74d470df45fd061bf71d42dc11af36300475fda7d3c03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-19T21:05:40Z","title_canon_sha256":"584b4557423c8fc9b447724de7d8fb45bf345acd52958d0dc4861af68dd8ba7d"},"schema_version":"1.0","source":{"id":"1402.4825","kind":"arxiv","version":1}},"canonical_sha256":"e046b912aedcd8bff233a4d8419178130943f89a606312bc9e9e02970206bfa5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e046b912aedcd8bff233a4d8419178130943f89a606312bc9e9e02970206bfa5","first_computed_at":"2026-05-18T02:58:32.042251Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:32.042251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NkGvmi+VzAAIu6c6MGTdtI1cVjfjEk9v1rtCP327XDu/Ug9gMUZyPv7o0j3DWwVnmnguoq7TRvCfY7+vZlMtAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:32.042794Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.4825","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:691faa2c36cc59ceee6ebb37f9146d0aa4c7b2e87cce80af9485a77df5fb724b","sha256:535a6b01c21c228276a927553a2d83fead08b2822db462d2af460e6b6c5c63d0"],"state_sha256":"2ef60ea70c6dda22a55fddb91890a2589e22c43d50a3869188d9a9ee882256a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PwOm7hSiMMTGp1WopXjOa5SRN/jEEZG01vktBbFXEpt/VFysVUGsNtpLIpqVmJFHC9OHnhCt6tgmIcAyCdNvAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T15:23:57.998172Z","bundle_sha256":"10519ef55534d0bd05dd81336e28e7c9055223f46c0b3b4cb7bd556f9681f665"}}