{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BM7MLP6RDSIXFXSGN5DZSRZEIV","short_pith_number":"pith:BM7MLP6R","canonical_record":{"source":{"id":"1307.3119","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-07-11T14:11:10Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"9cf8f46b53412d1c0946eb53a1d661d324b7be8e8b7531a5c69136e4c5aa443d","abstract_canon_sha256":"21a750ff6571abd90896114b683306ce1c2c9536c9dd6dd4c054e77ad810a2bf"},"schema_version":"1.0"},"canonical_sha256":"0b3ec5bfd11c9172de466f47994724456667defc408516d4425eee6b1e65fe76","source":{"kind":"arxiv","id":"1307.3119","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3119","created_at":"2026-05-18T03:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3119v1","created_at":"2026-05-18T03:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3119","created_at":"2026-05-18T03:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"BM7MLP6RDSIX","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BM7MLP6RDSIXFXSG","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BM7MLP6R","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BM7MLP6RDSIXFXSGN5DZSRZEIV","target":"record","payload":{"canonical_record":{"source":{"id":"1307.3119","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-07-11T14:11:10Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"9cf8f46b53412d1c0946eb53a1d661d324b7be8e8b7531a5c69136e4c5aa443d","abstract_canon_sha256":"21a750ff6571abd90896114b683306ce1c2c9536c9dd6dd4c054e77ad810a2bf"},"schema_version":"1.0"},"canonical_sha256":"0b3ec5bfd11c9172de466f47994724456667defc408516d4425eee6b1e65fe76","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:41.138543Z","signature_b64":"SvRC2fwexLKREFP09oWfLx6emQ1nO4J55G7MjRF3wvQSq/3iN1biIrzj5nRRN+y/Xr7qMTfCzfAVH/FsNuZRBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b3ec5bfd11c9172de466f47994724456667defc408516d4425eee6b1e65fe76","last_reissued_at":"2026-05-18T03:18:41.137667Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:41.137667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.3119","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":"2026-05-18T03:18:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uyeB2IfJRPeFn3RL4z+c2eIYn6slrXSmY73HuBpXi6cgpuBbrIaUIZjmuhJcmXF2KhdqfxL+dzbqf69CzjqhDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:07:16.909892Z"},"content_sha256":"176ebb0184f6a7cd82041f987e6c0b75f44bb953db22e01f2db01fcc9fd453b1","schema_version":"1.0","event_id":"sha256:176ebb0184f6a7cd82041f987e6c0b75f44bb953db22e01f2db01fcc9fd453b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BM7MLP6RDSIXFXSGN5DZSRZEIV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From homotopy to Ito calculus and Hodge theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.QA","authors_text":"Andrew Neate, Edwin Beggs, Ghaliah Alhamzi","submitted_at":"2013-07-11T14:11:10Z","abstract_excerpt":"We begin with a deformation of a differential graded algebra by adding time and using a homotopy. It is shown that the standard formulae of It\\^o calculus are an example, with four caveats: First, it says nothing about probability. Second, it assumes smooth functions. Third, it deforms all orders of forms, not just first order. Fourth, it also deforms the product of the DGA. An isomorphism between the deformed and original DGAs may be interpreted as the transformation rule between the Stratonovich and classical calculus (again no probability). The isomorphism can be used to construct covariant"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3119","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":"2026-05-18T03:18:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X75Vi9cgo84/T3UAXeVfGw90u8d7hibLUTP7ETp0QrxcFs8ZzdsHI+rzxgnwEWjq9dMaT8L7NlotuANWcDbbCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:07:16.910249Z"},"content_sha256":"ac5795a6976a91207cb4471ffc19742c68f2170ea46ed1853cc50825574c39eb","schema_version":"1.0","event_id":"sha256:ac5795a6976a91207cb4471ffc19742c68f2170ea46ed1853cc50825574c39eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BM7MLP6RDSIXFXSGN5DZSRZEIV/bundle.json","state_url":"https://pith.science/pith/BM7MLP6RDSIXFXSGN5DZSRZEIV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BM7MLP6RDSIXFXSGN5DZSRZEIV/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":"2026-05-31T20:07:16Z","links":{"resolver":"https://pith.science/pith/BM7MLP6RDSIXFXSGN5DZSRZEIV","bundle":"https://pith.science/pith/BM7MLP6RDSIXFXSGN5DZSRZEIV/bundle.json","state":"https://pith.science/pith/BM7MLP6RDSIXFXSGN5DZSRZEIV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BM7MLP6RDSIXFXSGN5DZSRZEIV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BM7MLP6RDSIXFXSGN5DZSRZEIV","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":"21a750ff6571abd90896114b683306ce1c2c9536c9dd6dd4c054e77ad810a2bf","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-07-11T14:11:10Z","title_canon_sha256":"9cf8f46b53412d1c0946eb53a1d661d324b7be8e8b7531a5c69136e4c5aa443d"},"schema_version":"1.0","source":{"id":"1307.3119","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3119","created_at":"2026-05-18T03:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3119v1","created_at":"2026-05-18T03:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3119","created_at":"2026-05-18T03:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"BM7MLP6RDSIX","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BM7MLP6RDSIXFXSG","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BM7MLP6R","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:ac5795a6976a91207cb4471ffc19742c68f2170ea46ed1853cc50825574c39eb","target":"graph","created_at":"2026-05-18T03:18:41Z","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":"We begin with a deformation of a differential graded algebra by adding time and using a homotopy. It is shown that the standard formulae of It\\^o calculus are an example, with four caveats: First, it says nothing about probability. Second, it assumes smooth functions. Third, it deforms all orders of forms, not just first order. Fourth, it also deforms the product of the DGA. An isomorphism between the deformed and original DGAs may be interpreted as the transformation rule between the Stratonovich and classical calculus (again no probability). The isomorphism can be used to construct covariant","authors_text":"Andrew Neate, Edwin Beggs, Ghaliah Alhamzi","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-07-11T14:11:10Z","title":"From homotopy to Ito calculus and Hodge theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3119","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":"sha256:176ebb0184f6a7cd82041f987e6c0b75f44bb953db22e01f2db01fcc9fd453b1","target":"record","created_at":"2026-05-18T03:18:41Z","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":"21a750ff6571abd90896114b683306ce1c2c9536c9dd6dd4c054e77ad810a2bf","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-07-11T14:11:10Z","title_canon_sha256":"9cf8f46b53412d1c0946eb53a1d661d324b7be8e8b7531a5c69136e4c5aa443d"},"schema_version":"1.0","source":{"id":"1307.3119","kind":"arxiv","version":1}},"canonical_sha256":"0b3ec5bfd11c9172de466f47994724456667defc408516d4425eee6b1e65fe76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b3ec5bfd11c9172de466f47994724456667defc408516d4425eee6b1e65fe76","first_computed_at":"2026-05-18T03:18:41.137667Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:41.137667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SvRC2fwexLKREFP09oWfLx6emQ1nO4J55G7MjRF3wvQSq/3iN1biIrzj5nRRN+y/Xr7qMTfCzfAVH/FsNuZRBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:41.138543Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.3119","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:176ebb0184f6a7cd82041f987e6c0b75f44bb953db22e01f2db01fcc9fd453b1","sha256:ac5795a6976a91207cb4471ffc19742c68f2170ea46ed1853cc50825574c39eb"],"state_sha256":"f1bc70f43d14e5cbc4a394488d3de8b00f63f01668a760b68bfd686ce66bbf30"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R78+mwfZJ4LmVK2UfP/CJ5aDwPSxIpjlxpzV7FNfpySulDtbaRcD/JkHbX7/OmSkjqH9o4X5ZcKeGGVk40HpDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T20:07:16.912615Z","bundle_sha256":"e4a8375a506ad1240f5f8cd416b1ef88cd8e2ba3e555102992db1398d6d7ea44"}}