{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:IPAQ3GSOPI3NYQC3INQY7RD4E4","short_pith_number":"pith:IPAQ3GSO","canonical_record":{"source":{"id":"1208.1189","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2012-08-06T15:22:00Z","cross_cats_sorted":[],"title_canon_sha256":"01d4c1bafcb1f19d52389f7fed4301c73da27c9a068e917e51b1ca5e9dca87a4","abstract_canon_sha256":"316c695162f37b6480073694709a49b9926b6fe800a13d3d457d45276a372a9e"},"schema_version":"1.0"},"canonical_sha256":"43c10d9a4e7a36dc405b43618fc47c27072c9bd0eeecd217e289cac34eb354b6","source":{"kind":"arxiv","id":"1208.1189","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1189","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1189v1","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1189","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"pith_short_12","alias_value":"IPAQ3GSOPI3N","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IPAQ3GSOPI3NYQC3","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IPAQ3GSO","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:IPAQ3GSOPI3NYQC3INQY7RD4E4","target":"record","payload":{"canonical_record":{"source":{"id":"1208.1189","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2012-08-06T15:22:00Z","cross_cats_sorted":[],"title_canon_sha256":"01d4c1bafcb1f19d52389f7fed4301c73da27c9a068e917e51b1ca5e9dca87a4","abstract_canon_sha256":"316c695162f37b6480073694709a49b9926b6fe800a13d3d457d45276a372a9e"},"schema_version":"1.0"},"canonical_sha256":"43c10d9a4e7a36dc405b43618fc47c27072c9bd0eeecd217e289cac34eb354b6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:20.404024Z","signature_b64":"m3eSQQPxXPSVF0Ufg05//gvCsLTaPaDjhZjUPmOTdcFthF3y6iRMxKerK6OWESy5n2kchI5xTHol32iA/lrhBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43c10d9a4e7a36dc405b43618fc47c27072c9bd0eeecd217e289cac34eb354b6","last_reissued_at":"2026-05-18T03:49:20.403200Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:20.403200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.1189","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":"2026-05-18T03:49:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CXMfLOIfhCsWktCr+JLA10wx+q92Jn3jnQ3zge5eU3BIhm0vqOOHGRYi5W+dBgu+uI+wP1mAlThrVRuu1aV3BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T16:53:23.501820Z"},"content_sha256":"f3a82a97ed1e8b370bdf3863cffd7d89ebccc67231d422e54cf609b5d1b4bada","schema_version":"1.0","event_id":"sha256:f3a82a97ed1e8b370bdf3863cffd7d89ebccc67231d422e54cf609b5d1b4bada"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:IPAQ3GSOPI3NYQC3INQY7RD4E4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mathematical Definition, Mapping, and Detection of (Anti)Fragility","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.RM","authors_text":"Nassim N. Taleb, Raphael Douady","submitted_at":"2012-08-06T15:22:00Z","abstract_excerpt":"We provide a mathematical definition of fragility and antifragility as negative or positive sensitivity to a semi-measure of dispersion and volatility (a variant of negative or positive \"vega\") and examine the link to nonlinear effects. We integrate model error (and biases) into the fragile or antifragile context. Unlike risk, which is linked to psychological notions such as subjective preferences (hence cannot apply to a coffee cup) we offer a measure that is universal and concerns any object that has a probability distribution (whether such distribution is known or, critically, unknown). We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1189","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":"2026-05-18T03:49:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ISj6rubZNffZhC7rVndhZGgIN9cmeNxo0s4WWJrWUveBMcwLI3dyfLE5SgFSwYF2JVQrCgz9MsXUyvzO2oUwBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T16:53:23.502157Z"},"content_sha256":"e5fab01dcf747c5f6703088f414ac3cba5bc77dc5c6fd90cf522cedb31f4f06c","schema_version":"1.0","event_id":"sha256:e5fab01dcf747c5f6703088f414ac3cba5bc77dc5c6fd90cf522cedb31f4f06c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IPAQ3GSOPI3NYQC3INQY7RD4E4/bundle.json","state_url":"https://pith.science/pith/IPAQ3GSOPI3NYQC3INQY7RD4E4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IPAQ3GSOPI3NYQC3INQY7RD4E4/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":"2026-06-25T16:53:23Z","links":{"resolver":"https://pith.science/pith/IPAQ3GSOPI3NYQC3INQY7RD4E4","bundle":"https://pith.science/pith/IPAQ3GSOPI3NYQC3INQY7RD4E4/bundle.json","state":"https://pith.science/pith/IPAQ3GSOPI3NYQC3INQY7RD4E4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IPAQ3GSOPI3NYQC3INQY7RD4E4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:IPAQ3GSOPI3NYQC3INQY7RD4E4","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":"316c695162f37b6480073694709a49b9926b6fe800a13d3d457d45276a372a9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2012-08-06T15:22:00Z","title_canon_sha256":"01d4c1bafcb1f19d52389f7fed4301c73da27c9a068e917e51b1ca5e9dca87a4"},"schema_version":"1.0","source":{"id":"1208.1189","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1189","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1189v1","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1189","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"pith_short_12","alias_value":"IPAQ3GSOPI3N","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IPAQ3GSOPI3NYQC3","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IPAQ3GSO","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:e5fab01dcf747c5f6703088f414ac3cba5bc77dc5c6fd90cf522cedb31f4f06c","target":"graph","created_at":"2026-05-18T03:49:20Z","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 provide a mathematical definition of fragility and antifragility as negative or positive sensitivity to a semi-measure of dispersion and volatility (a variant of negative or positive \"vega\") and examine the link to nonlinear effects. We integrate model error (and biases) into the fragile or antifragile context. Unlike risk, which is linked to psychological notions such as subjective preferences (hence cannot apply to a coffee cup) we offer a measure that is universal and concerns any object that has a probability distribution (whether such distribution is known or, critically, unknown). We ","authors_text":"Nassim N. Taleb, Raphael Douady","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2012-08-06T15:22:00Z","title":"Mathematical Definition, Mapping, and Detection of (Anti)Fragility"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1189","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:f3a82a97ed1e8b370bdf3863cffd7d89ebccc67231d422e54cf609b5d1b4bada","target":"record","created_at":"2026-05-18T03:49:20Z","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":"316c695162f37b6480073694709a49b9926b6fe800a13d3d457d45276a372a9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2012-08-06T15:22:00Z","title_canon_sha256":"01d4c1bafcb1f19d52389f7fed4301c73da27c9a068e917e51b1ca5e9dca87a4"},"schema_version":"1.0","source":{"id":"1208.1189","kind":"arxiv","version":1}},"canonical_sha256":"43c10d9a4e7a36dc405b43618fc47c27072c9bd0eeecd217e289cac34eb354b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43c10d9a4e7a36dc405b43618fc47c27072c9bd0eeecd217e289cac34eb354b6","first_computed_at":"2026-05-18T03:49:20.403200Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:20.403200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m3eSQQPxXPSVF0Ufg05//gvCsLTaPaDjhZjUPmOTdcFthF3y6iRMxKerK6OWESy5n2kchI5xTHol32iA/lrhBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:20.404024Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.1189","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3a82a97ed1e8b370bdf3863cffd7d89ebccc67231d422e54cf609b5d1b4bada","sha256:e5fab01dcf747c5f6703088f414ac3cba5bc77dc5c6fd90cf522cedb31f4f06c"],"state_sha256":"1130f28d92efb4d4d348ce3e557f02fb6a3833206ea6f99e506255e493ff7c8f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MZRM5vHIqaNxsXoEOfABVpH50BCPdkZu48tASX29h5z9DXBxlXo7ZSPxizRdgiWKZ8A6zAtRLy6heTo7a5ndCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T16:53:23.504065Z","bundle_sha256":"5b9a28ead529630f9656c89e689c693fd67fa77aa20bf70ed7a20cee51811f83"}}