{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:3PTCHIDWBAFDXHQANRZR5IF6G2","short_pith_number":"pith:3PTCHIDW","canonical_record":{"source":{"id":"1806.10838","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-28T09:19:08Z","cross_cats_sorted":[],"title_canon_sha256":"8a71e489d6925c4df9e7cf4f98f90157f4f6467849e168b435df75c75738d17e","abstract_canon_sha256":"2864c88553b596fb26d0ecc7933d218a78942539a39f0325f27bc623c6dcb87b"},"schema_version":"1.0"},"canonical_sha256":"dbe623a076080a3b9e006c731ea0be3682a8f04408f8f1b07bbe5352591b57b9","source":{"kind":"arxiv","id":"1806.10838","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10838","created_at":"2026-05-18T00:12:07Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10838v1","created_at":"2026-05-18T00:12:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10838","created_at":"2026-05-18T00:12:07Z"},{"alias_kind":"pith_short_12","alias_value":"3PTCHIDWBAFD","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3PTCHIDWBAFDXHQA","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3PTCHIDW","created_at":"2026-05-18T12:32:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:3PTCHIDWBAFDXHQANRZR5IF6G2","target":"record","payload":{"canonical_record":{"source":{"id":"1806.10838","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-28T09:19:08Z","cross_cats_sorted":[],"title_canon_sha256":"8a71e489d6925c4df9e7cf4f98f90157f4f6467849e168b435df75c75738d17e","abstract_canon_sha256":"2864c88553b596fb26d0ecc7933d218a78942539a39f0325f27bc623c6dcb87b"},"schema_version":"1.0"},"canonical_sha256":"dbe623a076080a3b9e006c731ea0be3682a8f04408f8f1b07bbe5352591b57b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:07.785310Z","signature_b64":"+T1ABYBMoyT5eGWxS46zNvRcTZFqBJK/vGL2js5DuxLC7r5U2ADVWxkzaK9ZIOjolwofq+1HKwGn8e7xWEKKBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dbe623a076080a3b9e006c731ea0be3682a8f04408f8f1b07bbe5352591b57b9","last_reissued_at":"2026-05-18T00:12:07.784740Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:07.784740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.10838","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":"2026-05-18T00:12:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yQhnJ6+TUNUDLA1i7deMNfeOMpv1IXShVmDlnsJziPPaw8kTRD1Z/NyHpKyOuHvDDUbSDiZIMloDKbPl1ygoDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:03:49.451421Z"},"content_sha256":"14c0aea82cdf6349f8b30bb1169c96177cb7544f3cacea47db50a64c96f5beb8","schema_version":"1.0","event_id":"sha256:14c0aea82cdf6349f8b30bb1169c96177cb7544f3cacea47db50a64c96f5beb8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:3PTCHIDWBAFDXHQANRZR5IF6G2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic Lipschitz regularity for tug-of-war games with varying probabilities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"\\'Angel Arroyo, Eero Ruosteenoja, Hannes Luiro, Mikko Parviainen","submitted_at":"2018-06-28T09:19:08Z","abstract_excerpt":"We prove an asymptotic Lipschitz estimate for value functions of tug-of-war games with varying probabilities defined in $\\Omega\\subset \\mathbb R^n$. The method of the proof is based on a game-theoretic idea to estimate the value of a related game defined in $\\Omega\\times \\Omega$ via couplings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10838","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":"2026-05-18T00:12:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NEEeiRV7+yz55qPwZ8gGIvmKQmk3yHJHswXStiz4aT9eLDkRxr/5zVaqJun8v5nw3zw+YxGkXVs6A97DnHJGDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:03:49.452112Z"},"content_sha256":"068882fbc6da310d2b7225289b3f54e745a3fce3fee04c39465f7b2b5d429a99","schema_version":"1.0","event_id":"sha256:068882fbc6da310d2b7225289b3f54e745a3fce3fee04c39465f7b2b5d429a99"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3PTCHIDWBAFDXHQANRZR5IF6G2/bundle.json","state_url":"https://pith.science/pith/3PTCHIDWBAFDXHQANRZR5IF6G2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3PTCHIDWBAFDXHQANRZR5IF6G2/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":"2026-06-09T12:03:49Z","links":{"resolver":"https://pith.science/pith/3PTCHIDWBAFDXHQANRZR5IF6G2","bundle":"https://pith.science/pith/3PTCHIDWBAFDXHQANRZR5IF6G2/bundle.json","state":"https://pith.science/pith/3PTCHIDWBAFDXHQANRZR5IF6G2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3PTCHIDWBAFDXHQANRZR5IF6G2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3PTCHIDWBAFDXHQANRZR5IF6G2","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":"2864c88553b596fb26d0ecc7933d218a78942539a39f0325f27bc623c6dcb87b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-28T09:19:08Z","title_canon_sha256":"8a71e489d6925c4df9e7cf4f98f90157f4f6467849e168b435df75c75738d17e"},"schema_version":"1.0","source":{"id":"1806.10838","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10838","created_at":"2026-05-18T00:12:07Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10838v1","created_at":"2026-05-18T00:12:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10838","created_at":"2026-05-18T00:12:07Z"},{"alias_kind":"pith_short_12","alias_value":"3PTCHIDWBAFD","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3PTCHIDWBAFDXHQA","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3PTCHIDW","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:068882fbc6da310d2b7225289b3f54e745a3fce3fee04c39465f7b2b5d429a99","target":"graph","created_at":"2026-05-18T00:12:07Z","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 prove an asymptotic Lipschitz estimate for value functions of tug-of-war games with varying probabilities defined in $\\Omega\\subset \\mathbb R^n$. The method of the proof is based on a game-theoretic idea to estimate the value of a related game defined in $\\Omega\\times \\Omega$ via couplings.","authors_text":"\\'Angel Arroyo, Eero Ruosteenoja, Hannes Luiro, Mikko Parviainen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-28T09:19:08Z","title":"Asymptotic Lipschitz regularity for tug-of-war games with varying probabilities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10838","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":"sha256:14c0aea82cdf6349f8b30bb1169c96177cb7544f3cacea47db50a64c96f5beb8","target":"record","created_at":"2026-05-18T00:12:07Z","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":"2864c88553b596fb26d0ecc7933d218a78942539a39f0325f27bc623c6dcb87b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-28T09:19:08Z","title_canon_sha256":"8a71e489d6925c4df9e7cf4f98f90157f4f6467849e168b435df75c75738d17e"},"schema_version":"1.0","source":{"id":"1806.10838","kind":"arxiv","version":1}},"canonical_sha256":"dbe623a076080a3b9e006c731ea0be3682a8f04408f8f1b07bbe5352591b57b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dbe623a076080a3b9e006c731ea0be3682a8f04408f8f1b07bbe5352591b57b9","first_computed_at":"2026-05-18T00:12:07.784740Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:07.784740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+T1ABYBMoyT5eGWxS46zNvRcTZFqBJK/vGL2js5DuxLC7r5U2ADVWxkzaK9ZIOjolwofq+1HKwGn8e7xWEKKBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:07.785310Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.10838","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14c0aea82cdf6349f8b30bb1169c96177cb7544f3cacea47db50a64c96f5beb8","sha256:068882fbc6da310d2b7225289b3f54e745a3fce3fee04c39465f7b2b5d429a99"],"state_sha256":"1bf7d4ea74c36e575e134725a48f9a7db5811e52365ac6eee8ac1776866bbfe5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2iRkZ28uBUO+h+IEBofFeTT1cCNfmTbXADqS+6GDxNU47ddtTemjqVhH1CbjEZU9lY1VMD36MaKvpISgjXnWDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T12:03:49.456291Z","bundle_sha256":"d0c1285394113e4319d664fd815bdc4404a6babd7dca1138487f8a026a1e9b27"}}