{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:SXVUUC5VHXZM3RFA6SLIQSS2IL","short_pith_number":"pith:SXVUUC5V","canonical_record":{"source":{"id":"1310.5675","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-21T19:00:43Z","cross_cats_sorted":[],"title_canon_sha256":"9e89321d3120b8cf4c0843993f7e80e7dc990c2db9aae0e45eb05bb3139f560f","abstract_canon_sha256":"b05172b82b597475161e3a607784e337c3abc18a26e50f13c8cdc8937c134d2d"},"schema_version":"1.0"},"canonical_sha256":"95eb4a0bb53df2cdc4a0f496884a5a42e5912b207d360e54c5658f541b2415ab","source":{"kind":"arxiv","id":"1310.5675","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.5675","created_at":"2026-05-18T03:09:34Z"},{"alias_kind":"arxiv_version","alias_value":"1310.5675v1","created_at":"2026-05-18T03:09:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5675","created_at":"2026-05-18T03:09:34Z"},{"alias_kind":"pith_short_12","alias_value":"SXVUUC5VHXZM","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SXVUUC5VHXZM3RFA","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SXVUUC5V","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:SXVUUC5VHXZM3RFA6SLIQSS2IL","target":"record","payload":{"canonical_record":{"source":{"id":"1310.5675","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-21T19:00:43Z","cross_cats_sorted":[],"title_canon_sha256":"9e89321d3120b8cf4c0843993f7e80e7dc990c2db9aae0e45eb05bb3139f560f","abstract_canon_sha256":"b05172b82b597475161e3a607784e337c3abc18a26e50f13c8cdc8937c134d2d"},"schema_version":"1.0"},"canonical_sha256":"95eb4a0bb53df2cdc4a0f496884a5a42e5912b207d360e54c5658f541b2415ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:34.557060Z","signature_b64":"7uN4SL3o3TTeTZjZs+JXXwtLJ/raXl6zazceFbdsVVzrx0PA45rqyfTUa/zg9P3H+K7W26jVTzeGUh77Vq0/DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95eb4a0bb53df2cdc4a0f496884a5a42e5912b207d360e54c5658f541b2415ab","last_reissued_at":"2026-05-18T03:09:34.556474Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:34.556474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.5675","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":"2026-05-18T03:09:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A1GXwXY7p/9lfGmuVDYRcQ3PrNv+xn/udGpjTecSs1zjHqd4/BX3iW5zCmvGlX11WJh7mwtNHNG/PTgLSBokCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T07:12:27.915884Z"},"content_sha256":"cec60a735ea76d85ae57d00a78e5b9c5944a8372ba3cb93d9c672adcbeaec6bb","schema_version":"1.0","event_id":"sha256:cec60a735ea76d85ae57d00a78e5b9c5944a8372ba3cb93d9c672adcbeaec6bb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:SXVUUC5VHXZM3RFA6SLIQSS2IL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A general study of extremes of stationary tessellations with applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Nicolas Chenavier","submitted_at":"2013-10-21T19:00:43Z","abstract_excerpt":"Let $\\mathfrak{m}$ be a random tessellation in $\\mathbf{R}^d$ observed in a bounded Borel subset $W$ and $f(\\cdot)$ be a measurable function defined on the set of convex bodies. To each cell $C$ of $\\mathfrak{m}$ we associate a point $z(C)$ which is the nucleus of $C$. Applying $f(\\cdot)$ to all the cells of $\\mathfrak{m}$, we investigate the order statistics of $f(C)$ over all cells $C\\in\\mathfrak{m}$ with nucleus in $\\mathbf{W}_{\\rho}=\\rho^{1/d}W$ when $\\rho$ goes to infinity. Under a strong mixing property and a local condition on $\\mathfrak{m}$ and $f(\\cdot)$, we show a general theorem whi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5675","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":"2026-05-18T03:09:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N7rWk3EN63R69EcPjQ9mzsSeNoYYD1JdVcCphxLWLotCgAZ+mJbion09Iosn3VuaaVoVmrwYujSpl/S7igQbDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T07:12:27.916484Z"},"content_sha256":"fd429323d3edd355505855306a4260e2581817659a8338ea2c6d08f9969d34f3","schema_version":"1.0","event_id":"sha256:fd429323d3edd355505855306a4260e2581817659a8338ea2c6d08f9969d34f3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SXVUUC5VHXZM3RFA6SLIQSS2IL/bundle.json","state_url":"https://pith.science/pith/SXVUUC5VHXZM3RFA6SLIQSS2IL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SXVUUC5VHXZM3RFA6SLIQSS2IL/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":"2026-06-05T07:12:27Z","links":{"resolver":"https://pith.science/pith/SXVUUC5VHXZM3RFA6SLIQSS2IL","bundle":"https://pith.science/pith/SXVUUC5VHXZM3RFA6SLIQSS2IL/bundle.json","state":"https://pith.science/pith/SXVUUC5VHXZM3RFA6SLIQSS2IL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SXVUUC5VHXZM3RFA6SLIQSS2IL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SXVUUC5VHXZM3RFA6SLIQSS2IL","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":"b05172b82b597475161e3a607784e337c3abc18a26e50f13c8cdc8937c134d2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-21T19:00:43Z","title_canon_sha256":"9e89321d3120b8cf4c0843993f7e80e7dc990c2db9aae0e45eb05bb3139f560f"},"schema_version":"1.0","source":{"id":"1310.5675","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.5675","created_at":"2026-05-18T03:09:34Z"},{"alias_kind":"arxiv_version","alias_value":"1310.5675v1","created_at":"2026-05-18T03:09:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5675","created_at":"2026-05-18T03:09:34Z"},{"alias_kind":"pith_short_12","alias_value":"SXVUUC5VHXZM","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SXVUUC5VHXZM3RFA","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SXVUUC5V","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:fd429323d3edd355505855306a4260e2581817659a8338ea2c6d08f9969d34f3","target":"graph","created_at":"2026-05-18T03:09:34Z","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":"Let $\\mathfrak{m}$ be a random tessellation in $\\mathbf{R}^d$ observed in a bounded Borel subset $W$ and $f(\\cdot)$ be a measurable function defined on the set of convex bodies. To each cell $C$ of $\\mathfrak{m}$ we associate a point $z(C)$ which is the nucleus of $C$. Applying $f(\\cdot)$ to all the cells of $\\mathfrak{m}$, we investigate the order statistics of $f(C)$ over all cells $C\\in\\mathfrak{m}$ with nucleus in $\\mathbf{W}_{\\rho}=\\rho^{1/d}W$ when $\\rho$ goes to infinity. Under a strong mixing property and a local condition on $\\mathfrak{m}$ and $f(\\cdot)$, we show a general theorem whi","authors_text":"Nicolas Chenavier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-21T19:00:43Z","title":"A general study of extremes of stationary tessellations with applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5675","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:cec60a735ea76d85ae57d00a78e5b9c5944a8372ba3cb93d9c672adcbeaec6bb","target":"record","created_at":"2026-05-18T03:09:34Z","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":"b05172b82b597475161e3a607784e337c3abc18a26e50f13c8cdc8937c134d2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-21T19:00:43Z","title_canon_sha256":"9e89321d3120b8cf4c0843993f7e80e7dc990c2db9aae0e45eb05bb3139f560f"},"schema_version":"1.0","source":{"id":"1310.5675","kind":"arxiv","version":1}},"canonical_sha256":"95eb4a0bb53df2cdc4a0f496884a5a42e5912b207d360e54c5658f541b2415ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95eb4a0bb53df2cdc4a0f496884a5a42e5912b207d360e54c5658f541b2415ab","first_computed_at":"2026-05-18T03:09:34.556474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:34.556474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7uN4SL3o3TTeTZjZs+JXXwtLJ/raXl6zazceFbdsVVzrx0PA45rqyfTUa/zg9P3H+K7W26jVTzeGUh77Vq0/DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:34.557060Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.5675","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cec60a735ea76d85ae57d00a78e5b9c5944a8372ba3cb93d9c672adcbeaec6bb","sha256:fd429323d3edd355505855306a4260e2581817659a8338ea2c6d08f9969d34f3"],"state_sha256":"92e20baacc5d8455621e72c6e186a4900af3698022f4f25fd4e330bab8393e12"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z3C3139v1cYkFZvNWA6/mXTNzOBuyDIV2MWkjNZcvqNHKL+HiiqLuCAg4hoyaaTvccqGQknM2aHrY+PCljZbBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T07:12:27.919757Z","bundle_sha256":"8f66af3fe1b122169b16869062ae5894e4363b680073517cd165c5ac98f3f8b0"}}