{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:MQE4DANIUBCU52SUA3JNNJXR24","short_pith_number":"pith:MQE4DANI","canonical_record":{"source":{"id":"1303.1284","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-03-06T09:38:15Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"a21cc944dc8af9173635fc34bc97ed5bf136032389e266ad5aa661926230c79b","abstract_canon_sha256":"f9599331270c90f7dd4cdb7c0b70ee3beaa769eb78133f539924219e8c62c2af"},"schema_version":"1.0"},"canonical_sha256":"6409c181a8a0454eea5406d2d6a6f1d712d0cb14ede7128673ec22b934178369","source":{"kind":"arxiv","id":"1303.1284","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1284","created_at":"2026-05-18T02:32:46Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1284v3","created_at":"2026-05-18T02:32:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1284","created_at":"2026-05-18T02:32:46Z"},{"alias_kind":"pith_short_12","alias_value":"MQE4DANIUBCU","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MQE4DANIUBCU52SU","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MQE4DANI","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:MQE4DANIUBCU52SUA3JNNJXR24","target":"record","payload":{"canonical_record":{"source":{"id":"1303.1284","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-03-06T09:38:15Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"a21cc944dc8af9173635fc34bc97ed5bf136032389e266ad5aa661926230c79b","abstract_canon_sha256":"f9599331270c90f7dd4cdb7c0b70ee3beaa769eb78133f539924219e8c62c2af"},"schema_version":"1.0"},"canonical_sha256":"6409c181a8a0454eea5406d2d6a6f1d712d0cb14ede7128673ec22b934178369","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:46.532304Z","signature_b64":"BtlzxZr66/yA9OBNgN5gWmMvtHyb0bh66DKhYQ1vEWL4Qwv2xF/ZU0EkBr5rzb/Aqs7mJ45OMYf7+OkqrqQ2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6409c181a8a0454eea5406d2d6a6f1d712d0cb14ede7128673ec22b934178369","last_reissued_at":"2026-05-18T02:32:46.531850Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:46.531850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.1284","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:32:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3LjCyxt5P3gIpV1S3OUAObmKU+DCew1sHjhbqyzumYD+3ib6Cr1LRWDd3QrIgCk1pf75fih3VpOdXOQ8++VXBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T09:29:51.368994Z"},"content_sha256":"80541a4e0e8f87471be469faf24178a10eb14e357f6ca999d12762677ae87249","schema_version":"1.0","event_id":"sha256:80541a4e0e8f87471be469faf24178a10eb14e357f6ca999d12762677ae87249"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:MQE4DANIUBCU52SUA3JNNJXR24","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Idempotent D-Norms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Michael Falk","submitted_at":"2013-03-06T09:38:15Z","abstract_excerpt":"Replacing the spectral measure by a random vector $\\bfZ$ allows the representation of a max-stable distribution on $\\R^d$ with standard negative margins via a norm, called \\emph{$D$-norm}, whose generator is $\\bfZ$. The set of $D$-norms can be equipped with a commutative multiplication type operation, making it a semigroup with an identity element. This multiplication leads to idempotent $D$-norms. We characterize the set of idempotent $D$-norms. Iterating the multiplication provides a track of $D$-norms, whose limit exists and is again a $D$-norm. If this iteration is repeatedly done on the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1284","kind":"arxiv","version":3},"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":"2026-05-18T02:32:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KuJpRzXeEpQKtKzOYneDXVJt5VP+Kah3jyyY6aqf8sbhrumJvjYtGxq7NBzFzzvISKg81Zwx7/+l7/8pT7WMBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T09:29:51.369351Z"},"content_sha256":"6781964612132c9b239acb1d3e6c7c489c07909df5df4752062e9e392eac6966","schema_version":"1.0","event_id":"sha256:6781964612132c9b239acb1d3e6c7c489c07909df5df4752062e9e392eac6966"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MQE4DANIUBCU52SUA3JNNJXR24/bundle.json","state_url":"https://pith.science/pith/MQE4DANIUBCU52SUA3JNNJXR24/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MQE4DANIUBCU52SUA3JNNJXR24/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":"2026-06-20T09:29:51Z","links":{"resolver":"https://pith.science/pith/MQE4DANIUBCU52SUA3JNNJXR24","bundle":"https://pith.science/pith/MQE4DANIUBCU52SUA3JNNJXR24/bundle.json","state":"https://pith.science/pith/MQE4DANIUBCU52SUA3JNNJXR24/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MQE4DANIUBCU52SUA3JNNJXR24/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MQE4DANIUBCU52SUA3JNNJXR24","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":"f9599331270c90f7dd4cdb7c0b70ee3beaa769eb78133f539924219e8c62c2af","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-03-06T09:38:15Z","title_canon_sha256":"a21cc944dc8af9173635fc34bc97ed5bf136032389e266ad5aa661926230c79b"},"schema_version":"1.0","source":{"id":"1303.1284","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1284","created_at":"2026-05-18T02:32:46Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1284v3","created_at":"2026-05-18T02:32:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1284","created_at":"2026-05-18T02:32:46Z"},{"alias_kind":"pith_short_12","alias_value":"MQE4DANIUBCU","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MQE4DANIUBCU52SU","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MQE4DANI","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:6781964612132c9b239acb1d3e6c7c489c07909df5df4752062e9e392eac6966","target":"graph","created_at":"2026-05-18T02:32:46Z","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":"Replacing the spectral measure by a random vector $\\bfZ$ allows the representation of a max-stable distribution on $\\R^d$ with standard negative margins via a norm, called \\emph{$D$-norm}, whose generator is $\\bfZ$. The set of $D$-norms can be equipped with a commutative multiplication type operation, making it a semigroup with an identity element. This multiplication leads to idempotent $D$-norms. We characterize the set of idempotent $D$-norms. Iterating the multiplication provides a track of $D$-norms, whose limit exists and is again a $D$-norm. If this iteration is repeatedly done on the s","authors_text":"Michael Falk","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-03-06T09:38:15Z","title":"On Idempotent D-Norms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1284","kind":"arxiv","version":3},"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":"sha256:80541a4e0e8f87471be469faf24178a10eb14e357f6ca999d12762677ae87249","target":"record","created_at":"2026-05-18T02:32:46Z","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":"f9599331270c90f7dd4cdb7c0b70ee3beaa769eb78133f539924219e8c62c2af","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-03-06T09:38:15Z","title_canon_sha256":"a21cc944dc8af9173635fc34bc97ed5bf136032389e266ad5aa661926230c79b"},"schema_version":"1.0","source":{"id":"1303.1284","kind":"arxiv","version":3}},"canonical_sha256":"6409c181a8a0454eea5406d2d6a6f1d712d0cb14ede7128673ec22b934178369","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6409c181a8a0454eea5406d2d6a6f1d712d0cb14ede7128673ec22b934178369","first_computed_at":"2026-05-18T02:32:46.531850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:46.531850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BtlzxZr66/yA9OBNgN5gWmMvtHyb0bh66DKhYQ1vEWL4Qwv2xF/ZU0EkBr5rzb/Aqs7mJ45OMYf7+OkqrqQ2Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:46.532304Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.1284","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80541a4e0e8f87471be469faf24178a10eb14e357f6ca999d12762677ae87249","sha256:6781964612132c9b239acb1d3e6c7c489c07909df5df4752062e9e392eac6966"],"state_sha256":"eb6dadc70738aa655b5efef97fa1b82c3450483429412804fccbfbf41e747604"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gnyk7SqPficUYVhf8AuIcimpcmFD6cohVS/gpvHPU65N82mgFJZRA46WFtlTPydp7j7F6W4GYM7CGmsP4obeBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T09:29:51.371343Z","bundle_sha256":"090153a3d353ad6e2c04f9595b4fee560344efc92ab82f96fcbe0187c93cf2bd"}}