{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LXNAL6SUC23TMEPLEIGCV4UTLA","short_pith_number":"pith:LXNAL6SU","canonical_record":{"source":{"id":"1501.03598","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-15T08:23:07Z","cross_cats_sorted":[],"title_canon_sha256":"18ed15fcaf7430259e4d9822a14d07377f7801e20951fa504f94fbdf9d82630b","abstract_canon_sha256":"e26fbe8e5773f106c8ab07e06af3c16b523289ede8052898010ca53948787b2e"},"schema_version":"1.0"},"canonical_sha256":"5dda05fa5416b73611eb220c2af293582627e8e55416a16c396881d54784b097","source":{"kind":"arxiv","id":"1501.03598","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.03598","created_at":"2026-05-18T02:29:18Z"},{"alias_kind":"arxiv_version","alias_value":"1501.03598v1","created_at":"2026-05-18T02:29:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03598","created_at":"2026-05-18T02:29:18Z"},{"alias_kind":"pith_short_12","alias_value":"LXNAL6SUC23T","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LXNAL6SUC23TMEPL","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LXNAL6SU","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LXNAL6SUC23TMEPLEIGCV4UTLA","target":"record","payload":{"canonical_record":{"source":{"id":"1501.03598","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-15T08:23:07Z","cross_cats_sorted":[],"title_canon_sha256":"18ed15fcaf7430259e4d9822a14d07377f7801e20951fa504f94fbdf9d82630b","abstract_canon_sha256":"e26fbe8e5773f106c8ab07e06af3c16b523289ede8052898010ca53948787b2e"},"schema_version":"1.0"},"canonical_sha256":"5dda05fa5416b73611eb220c2af293582627e8e55416a16c396881d54784b097","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:18.180453Z","signature_b64":"PPw/kM325tV0uZeSjVlHUgE30S6G+4FQARGmld7LyG2cVLU9rmEHktgEe4LFZzpIgZENGF8buEtI+FVnpEruDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5dda05fa5416b73611eb220c2af293582627e8e55416a16c396881d54784b097","last_reissued_at":"2026-05-18T02:29:18.179987Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:18.179987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.03598","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":"2026-05-18T02:29:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vN7WP4lk9IzhG/nbX8jjQJhjaTLNYNVLYXXvN72i1d2tMs0k2YEiYY9KhQbqvnPyg0MEGwVfnW2jewBZfP+sDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:29:20.380259Z"},"content_sha256":"656e872aff6b70ec2c5cc15071d4ff0e78072f42be9b684904f2c3a594841a6e","schema_version":"1.0","event_id":"sha256:656e872aff6b70ec2c5cc15071d4ff0e78072f42be9b684904f2c3a594841a6e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LXNAL6SUC23TMEPLEIGCV4UTLA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global heat kernel estimates for symmetric Markov processes dominated by stable-like processes in exterior $C^{1,\\eta}$ open sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kyung-Youn Kim","submitted_at":"2015-01-15T08:23:07Z","abstract_excerpt":"In this paper, we establish sharp two-sided heat kernel estimates for a large class of symmetric Markov processes in exterior $C^{1,\\eta}$ open sets for all $t> 0$. The processes are symmetric pure jump Markov processes with jumping kernel intensity $$\\kappa(x, y)\\psi(|x-y|)^{-1}|x-y|^{-d-\\alpha}$$ where $\\alpha\\in(0,2)$, $\\psi$ is an increasing function on $[ 0, \\infty)$ with $\\psi(r)=1$ on $0<r\\le 1$ and $c_1e^{c_2r^{\\beta}}\\le \\psi(r)\\le c_3e^{c_4r^{\\beta}}$ on $r>1$ for $\\beta\\in[0, \\infty]$. A symmetric function $\\kappa(x, y)$ is bounded by two positive constants and $|\\kappa(x, y)-\\kappa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03598","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":"2026-05-18T02:29:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1KRsp/ybp16XM0THXEfuil2vUb6CM/kha1EQGVXYQF5kX4IRuhXoM6+YphBw9inhY07tILVgdAemZXf9KJ/9CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:29:20.380700Z"},"content_sha256":"735a74378f6f511181d910443be88317f50845914e871be529c450af5ca4c18e","schema_version":"1.0","event_id":"sha256:735a74378f6f511181d910443be88317f50845914e871be529c450af5ca4c18e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LXNAL6SUC23TMEPLEIGCV4UTLA/bundle.json","state_url":"https://pith.science/pith/LXNAL6SUC23TMEPLEIGCV4UTLA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LXNAL6SUC23TMEPLEIGCV4UTLA/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":"2026-06-25T18:29:20Z","links":{"resolver":"https://pith.science/pith/LXNAL6SUC23TMEPLEIGCV4UTLA","bundle":"https://pith.science/pith/LXNAL6SUC23TMEPLEIGCV4UTLA/bundle.json","state":"https://pith.science/pith/LXNAL6SUC23TMEPLEIGCV4UTLA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LXNAL6SUC23TMEPLEIGCV4UTLA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LXNAL6SUC23TMEPLEIGCV4UTLA","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":"e26fbe8e5773f106c8ab07e06af3c16b523289ede8052898010ca53948787b2e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-15T08:23:07Z","title_canon_sha256":"18ed15fcaf7430259e4d9822a14d07377f7801e20951fa504f94fbdf9d82630b"},"schema_version":"1.0","source":{"id":"1501.03598","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.03598","created_at":"2026-05-18T02:29:18Z"},{"alias_kind":"arxiv_version","alias_value":"1501.03598v1","created_at":"2026-05-18T02:29:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03598","created_at":"2026-05-18T02:29:18Z"},{"alias_kind":"pith_short_12","alias_value":"LXNAL6SUC23T","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LXNAL6SUC23TMEPL","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LXNAL6SU","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:735a74378f6f511181d910443be88317f50845914e871be529c450af5ca4c18e","target":"graph","created_at":"2026-05-18T02:29:18Z","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":"In this paper, we establish sharp two-sided heat kernel estimates for a large class of symmetric Markov processes in exterior $C^{1,\\eta}$ open sets for all $t> 0$. The processes are symmetric pure jump Markov processes with jumping kernel intensity $$\\kappa(x, y)\\psi(|x-y|)^{-1}|x-y|^{-d-\\alpha}$$ where $\\alpha\\in(0,2)$, $\\psi$ is an increasing function on $[ 0, \\infty)$ with $\\psi(r)=1$ on $0<r\\le 1$ and $c_1e^{c_2r^{\\beta}}\\le \\psi(r)\\le c_3e^{c_4r^{\\beta}}$ on $r>1$ for $\\beta\\in[0, \\infty]$. A symmetric function $\\kappa(x, y)$ is bounded by two positive constants and $|\\kappa(x, y)-\\kappa","authors_text":"Kyung-Youn Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-15T08:23:07Z","title":"Global heat kernel estimates for symmetric Markov processes dominated by stable-like processes in exterior $C^{1,\\eta}$ open sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03598","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":"sha256:656e872aff6b70ec2c5cc15071d4ff0e78072f42be9b684904f2c3a594841a6e","target":"record","created_at":"2026-05-18T02:29:18Z","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":"e26fbe8e5773f106c8ab07e06af3c16b523289ede8052898010ca53948787b2e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-15T08:23:07Z","title_canon_sha256":"18ed15fcaf7430259e4d9822a14d07377f7801e20951fa504f94fbdf9d82630b"},"schema_version":"1.0","source":{"id":"1501.03598","kind":"arxiv","version":1}},"canonical_sha256":"5dda05fa5416b73611eb220c2af293582627e8e55416a16c396881d54784b097","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5dda05fa5416b73611eb220c2af293582627e8e55416a16c396881d54784b097","first_computed_at":"2026-05-18T02:29:18.179987Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:18.179987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PPw/kM325tV0uZeSjVlHUgE30S6G+4FQARGmld7LyG2cVLU9rmEHktgEe4LFZzpIgZENGF8buEtI+FVnpEruDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:18.180453Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.03598","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:656e872aff6b70ec2c5cc15071d4ff0e78072f42be9b684904f2c3a594841a6e","sha256:735a74378f6f511181d910443be88317f50845914e871be529c450af5ca4c18e"],"state_sha256":"0c9109ab8bf254e20e6bb4dfc5989344153f463423071fb39157f232ed50284e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UuBv04O7y1cpSOoHT1s1/HvITpBzsFmAL7Fs23jVXFyME/p9Zb8PDfRMuCJPm1K976KZtYPaEThGKJU0LTZECw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T18:29:20.382785Z","bundle_sha256":"9f738ca265e5c47d2441706c5681feb3aca6cf2a19e9d49a87904699acb7c28c"}}