{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:UHY5MCEBVWV44AYBHIXFJRCERQ","short_pith_number":"pith:UHY5MCEB","schema_version":"1.0","canonical_sha256":"a1f1d60881adabce03013a2e54c4448c35f6b8a78556e7cd36a9883be7abfef8","source":{"kind":"arxiv","id":"1605.03551","version":1},"attestation_state":"computed","paper":{"title":"Global Gauge Symmetries, Risk-Free Portfolios, and the Risk-Free Rate","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.PR"],"primary_cat":"q-fin.GN","authors_text":"Martin Gremm","submitted_at":"2016-05-11T19:04:27Z","abstract_excerpt":"We define risk-free portfolios using three gauge invariant differential operators that require such portfolios to be insensitive to price changes, to be self-financing, and to produce a zero real return so there are no risk-free profits. This definition identifies the risk-free rate as the return of an infinitely diversified portfolio rather than as an arbitrary external parameter. The risk-free rate measures the rate of global price rescaling, which is a gauge symmetry of economies. We explore the properties of risk-free rates, rederive the Black Scholes equation with a new interpretation of "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1605.03551","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.GN","submitted_at":"2016-05-11T19:04:27Z","cross_cats_sorted":["q-fin.PR"],"title_canon_sha256":"bc06ab6f2dcf26700f027fe28d672de99fca1121ee1985e3c0b34bd37062c7e8","abstract_canon_sha256":"027b04f1337c390e434db61badb1ec361a848735597314880534a3d89a5da522"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:01.140836Z","signature_b64":"uTDkB48GsWobotBr3psCUWn+h3Cq2L2ffifhA4YOv6RANOXx6QCfKyNR/+1Q2PtXOq6EJIDVEqARHYE4ob4IBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1f1d60881adabce03013a2e54c4448c35f6b8a78556e7cd36a9883be7abfef8","last_reissued_at":"2026-05-18T01:15:01.140225Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:01.140225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global Gauge Symmetries, Risk-Free Portfolios, and the Risk-Free Rate","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.PR"],"primary_cat":"q-fin.GN","authors_text":"Martin Gremm","submitted_at":"2016-05-11T19:04:27Z","abstract_excerpt":"We define risk-free portfolios using three gauge invariant differential operators that require such portfolios to be insensitive to price changes, to be self-financing, and to produce a zero real return so there are no risk-free profits. This definition identifies the risk-free rate as the return of an infinitely diversified portfolio rather than as an arbitrary external parameter. The risk-free rate measures the rate of global price rescaling, which is a gauge symmetry of economies. We explore the properties of risk-free rates, rederive the Black Scholes equation with a new interpretation of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03551","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1605.03551","created_at":"2026-05-18T01:15:01.140312+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.03551v1","created_at":"2026-05-18T01:15:01.140312+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03551","created_at":"2026-05-18T01:15:01.140312+00:00"},{"alias_kind":"pith_short_12","alias_value":"UHY5MCEBVWV4","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"UHY5MCEBVWV44AYB","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"UHY5MCEB","created_at":"2026-05-18T12:30:46.583412+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UHY5MCEBVWV44AYBHIXFJRCERQ","json":"https://pith.science/pith/UHY5MCEBVWV44AYBHIXFJRCERQ.json","graph_json":"https://pith.science/api/pith-number/UHY5MCEBVWV44AYBHIXFJRCERQ/graph.json","events_json":"https://pith.science/api/pith-number/UHY5MCEBVWV44AYBHIXFJRCERQ/events.json","paper":"https://pith.science/paper/UHY5MCEB"},"agent_actions":{"view_html":"https://pith.science/pith/UHY5MCEBVWV44AYBHIXFJRCERQ","download_json":"https://pith.science/pith/UHY5MCEBVWV44AYBHIXFJRCERQ.json","view_paper":"https://pith.science/paper/UHY5MCEB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.03551&json=true","fetch_graph":"https://pith.science/api/pith-number/UHY5MCEBVWV44AYBHIXFJRCERQ/graph.json","fetch_events":"https://pith.science/api/pith-number/UHY5MCEBVWV44AYBHIXFJRCERQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UHY5MCEBVWV44AYBHIXFJRCERQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UHY5MCEBVWV44AYBHIXFJRCERQ/action/storage_attestation","attest_author":"https://pith.science/pith/UHY5MCEBVWV44AYBHIXFJRCERQ/action/author_attestation","sign_citation":"https://pith.science/pith/UHY5MCEBVWV44AYBHIXFJRCERQ/action/citation_signature","submit_replication":"https://pith.science/pith/UHY5MCEBVWV44AYBHIXFJRCERQ/action/replication_record"}},"created_at":"2026-05-18T01:15:01.140312+00:00","updated_at":"2026-05-18T01:15:01.140312+00:00"}