{"id":"https://openalex.org/W7118771641","doi":"https://doi.org/10.48550/arxiv.2601.00816","title":"MathLedger: A Verifiable Learning Substrate with Ledger-Attested Feedback","display_name":"MathLedger: A Verifiable Learning Substrate with Ledger-Attested Feedback","publication_year":2025,"publication_date":"2025-12-22","ids":{"openalex":"https://openalex.org/W7118771641","doi":"https://doi.org/10.48550/arxiv.2601.00816"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2601.00816","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.00816","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2601.00816","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5122209373","display_name":"Ismail Ahmad Abdullah","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Abdullah, Ismail Ahmad","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5122209373"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.945900022983551,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.945900022983551,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.0071000000461936,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10883","display_name":"Ethics and Social Impacts of AI","score":0.005499999970197678,"subfield":{"id":"https://openalex.org/subfields/3311","display_name":"Safety Research"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/verifiable-secret-sharing","display_name":"Verifiable secret sharing","score":0.858299970626831},{"id":"https://openalex.org/keywords/reflexivity","display_name":"Reflexivity","score":0.6061999797821045},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.527999997138977},{"id":"https://openalex.org/keywords/cryptographic-primitive","display_name":"Cryptographic primitive","score":0.44429999589920044},{"id":"https://openalex.org/keywords/cryptographic-protocol","display_name":"Cryptographic protocol","score":0.44350001215934753},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.4332999885082245},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.4000000059604645}],"concepts":[{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.858299970626831},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6366999745368958},{"id":"https://openalex.org/C13200473","wikidata":"https://www.wikidata.org/wiki/Q2747831","display_name":"Reflexivity","level":2,"score":0.6061999797821045},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.527999997138977},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.49149999022483826},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.45649999380111694},{"id":"https://openalex.org/C15927051","wikidata":"https://www.wikidata.org/wiki/Q246593","display_name":"Cryptographic primitive","level":4,"score":0.44429999589920044},{"id":"https://openalex.org/C33884865","wikidata":"https://www.wikidata.org/wiki/Q1254335","display_name":"Cryptographic protocol","level":3,"score":0.44350001215934753},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.4332999885082245},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.4000000059604645},{"id":"https://openalex.org/C2777289219","wikidata":"https://www.wikidata.org/wiki/Q7632154","display_name":"Substrate (aquarium)","level":2,"score":0.3873000144958496},{"id":"https://openalex.org/C2780385302","wikidata":"https://www.wikidata.org/wiki/Q367158","display_name":"Protocol (science)","level":3,"score":0.3831000030040741},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.3716000020503998},{"id":"https://openalex.org/C39389867","wikidata":"https://www.wikidata.org/wiki/Q380767","display_name":"Corporate governance","level":2,"score":0.3646000027656555},{"id":"https://openalex.org/C2779696439","wikidata":"https://www.wikidata.org/wiki/Q7512811","display_name":"Signature (topology)","level":2,"score":0.351500004529953},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.3391000032424927},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.33390000462532043},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.3285999894142151},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3246000111103058},{"id":"https://openalex.org/C191287063","wikidata":"https://www.wikidata.org/wiki/Q543281","display_name":"Glitch","level":3,"score":0.2930999994277954},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.28439998626708984},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26350000500679016}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2601.00816","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.00816","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2601.00816","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.00816","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"score":0.6224415898323059,"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Contemporary":[0],"AI":[1],"systems":[2],"achieve":[3],"extraordinary":[4],"performance":[5],"yet":[6],"remain":[7],"opaque":[8],"and":[9,34,72],"non-verifiable,":[10],"creating":[11],"a":[12,22,38,49,109],"crisis":[13],"of":[14,52,112],"trust":[15],"for":[16,24],"safety-critical":[17],"deployment.":[18],"We":[19],"introduce":[20],"MathLedger,":[21],"substrate":[23,74],"verifiable":[25,121],"machine":[26],"cognition":[27],"that":[28,115],"integrates":[29],"formal":[30,123],"verification,":[31,124],"cryptographic":[32,125],"attestation,":[33,126],"learning":[35,114],"dynamics":[36],"into":[37],"single":[39],"epistemic":[40],"loop.":[41],"The":[42,105],"system":[43],"implements":[44],"Reflexive":[45],"Formal":[46],"Learning":[47],"(RFL),":[48],"symbolic":[50],"analogue":[51],"gradient":[53],"descent":[54],"where":[55],"updates":[56],"are":[57,103],"driven":[58],"by":[59],"verifier":[60],"outcomes":[61],"rather":[62],"than":[63],"statistical":[64],"loss.":[65],"Phase":[66],"I":[67],"experiments":[68],"validate":[69],"the":[70],"measurement":[71,80],"governance":[73,92,130],"under":[75,95],"controlled":[76],"conditions.":[77,97],"CAL-EXP-3":[78],"validates":[79],"infrastructure":[81],"(Delta":[82],"p":[83],"computation,":[84],"variance":[85],"tracking);":[86],"separate":[87],"stress":[88],"tests":[89],"confirm":[90],"fail-closed":[91,129],"triggers":[93],"correctly":[94],"out-of-bounds":[96],"No":[98],"convergence":[99],"or":[100],"capability":[101],"claims":[102],"made.":[104],"contribution":[106],"is":[107],"infrastructural:":[108],"working":[110],"prototype":[111],"ledger-attested":[113],"enables":[116],"auditability":[117],"at":[118],"scale.":[119],"Keywords:":[120],"learning,":[122],"reflexive":[127],"feedback,":[128]},"counts_by_year":[],"updated_date":"2026-01-08T20:10:11.968330","created_date":"2026-01-08T00:00:00"}