{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GJQ4BCHTVE6OKXBBSHLIX46653","short_pith_number":"pith:GJQ4BCHT","canonical_record":{"source":{"id":"1102.4470","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-22T11:32:47Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"afafe2aecef7e58bb48fa9a4263f7a78073fd45efdadeb7146275b9a6e6f281b","abstract_canon_sha256":"f1ecc7a2038830110364497de95ca8abc7c8230ec0133ff147353aa60412b603"},"schema_version":"1.0"},"canonical_sha256":"3261c088f3a93ce55c2191d68bf3deeec210176f1e552cabcb573d744f27b0d7","source":{"kind":"arxiv","id":"1102.4470","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4470","created_at":"2026-05-18T02:03:06Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4470v1","created_at":"2026-05-18T02:03:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4470","created_at":"2026-05-18T02:03:06Z"},{"alias_kind":"pith_short_12","alias_value":"GJQ4BCHTVE6O","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GJQ4BCHTVE6OKXBB","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GJQ4BCHT","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GJQ4BCHTVE6OKXBBSHLIX46653","target":"record","payload":{"canonical_record":{"source":{"id":"1102.4470","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-22T11:32:47Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"afafe2aecef7e58bb48fa9a4263f7a78073fd45efdadeb7146275b9a6e6f281b","abstract_canon_sha256":"f1ecc7a2038830110364497de95ca8abc7c8230ec0133ff147353aa60412b603"},"schema_version":"1.0"},"canonical_sha256":"3261c088f3a93ce55c2191d68bf3deeec210176f1e552cabcb573d744f27b0d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:06.559671Z","signature_b64":"GkWyHF4dQVHo0HSp4MjPtW4tCj7cyeDIWWkz5TJLWdG7eW5tLySKodw/a0ID2CJnZGbrF0G5wcew5jF6gYS0BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3261c088f3a93ce55c2191d68bf3deeec210176f1e552cabcb573d744f27b0d7","last_reissued_at":"2026-05-18T02:03:06.559147Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:06.559147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.4470","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":"2026-05-18T02:03:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ukx9DmPPwNB2hzVKoENFE3Psj01IgHwcwEWH83K05nDdHbCPGcRhNYx0iOraMi1q7h5puGxCpl1Ze1bgelWvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:29:54.746673Z"},"content_sha256":"92d18a0021c8150b1711d29d2c395ca6f33859a6fc86228dfd91db014d5b7c5b","schema_version":"1.0","event_id":"sha256:92d18a0021c8150b1711d29d2c395ca6f33859a6fc86228dfd91db014d5b7c5b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GJQ4BCHTVE6OKXBBSHLIX46653","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on the abelian sandpile in Z^d","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.CO","authors_text":"Mykhaylo Tyomkyn","submitted_at":"2011-02-22T11:32:47Z","abstract_excerpt":"We analyse the abelian sandpile model on $\\mathbbm{Z}^d$ for the starting configuration of $n$ particles in the origin and $2d-2$ particles otherwise. We give a new short proof of the theorem of Fey, Levine and Peres \\cite{FLP} that the radius of the toppled cluster of this configuration is $O(n^{1/d})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4470","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":"2026-05-18T02:03:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+RHOuMYYoQ/qKsYT3LL3DoAaU3PCo/iSYBnf9tfNXni+W7qTvfYJ731UKjNaJ+zzsGH3UkVFaQgjZKFSpzAZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:29:54.747021Z"},"content_sha256":"6e0d48a1eba4dc9286f9cef092da55a19b9ee656cad4634fde50e5bb70838d5d","schema_version":"1.0","event_id":"sha256:6e0d48a1eba4dc9286f9cef092da55a19b9ee656cad4634fde50e5bb70838d5d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GJQ4BCHTVE6OKXBBSHLIX46653/bundle.json","state_url":"https://pith.science/pith/GJQ4BCHTVE6OKXBBSHLIX46653/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GJQ4BCHTVE6OKXBBSHLIX46653/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":"2026-06-03T06:29:54Z","links":{"resolver":"https://pith.science/pith/GJQ4BCHTVE6OKXBBSHLIX46653","bundle":"https://pith.science/pith/GJQ4BCHTVE6OKXBBSHLIX46653/bundle.json","state":"https://pith.science/pith/GJQ4BCHTVE6OKXBBSHLIX46653/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GJQ4BCHTVE6OKXBBSHLIX46653/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GJQ4BCHTVE6OKXBBSHLIX46653","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":"f1ecc7a2038830110364497de95ca8abc7c8230ec0133ff147353aa60412b603","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-22T11:32:47Z","title_canon_sha256":"afafe2aecef7e58bb48fa9a4263f7a78073fd45efdadeb7146275b9a6e6f281b"},"schema_version":"1.0","source":{"id":"1102.4470","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4470","created_at":"2026-05-18T02:03:06Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4470v1","created_at":"2026-05-18T02:03:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4470","created_at":"2026-05-18T02:03:06Z"},{"alias_kind":"pith_short_12","alias_value":"GJQ4BCHTVE6O","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GJQ4BCHTVE6OKXBB","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GJQ4BCHT","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:6e0d48a1eba4dc9286f9cef092da55a19b9ee656cad4634fde50e5bb70838d5d","target":"graph","created_at":"2026-05-18T02:03:06Z","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 analyse the abelian sandpile model on $\\mathbbm{Z}^d$ for the starting configuration of $n$ particles in the origin and $2d-2$ particles otherwise. We give a new short proof of the theorem of Fey, Levine and Peres \\cite{FLP} that the radius of the toppled cluster of this configuration is $O(n^{1/d})$.","authors_text":"Mykhaylo Tyomkyn","cross_cats":["math-ph","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-22T11:32:47Z","title":"A note on the abelian sandpile in Z^d"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4470","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":"sha256:92d18a0021c8150b1711d29d2c395ca6f33859a6fc86228dfd91db014d5b7c5b","target":"record","created_at":"2026-05-18T02:03:06Z","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":"f1ecc7a2038830110364497de95ca8abc7c8230ec0133ff147353aa60412b603","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-22T11:32:47Z","title_canon_sha256":"afafe2aecef7e58bb48fa9a4263f7a78073fd45efdadeb7146275b9a6e6f281b"},"schema_version":"1.0","source":{"id":"1102.4470","kind":"arxiv","version":1}},"canonical_sha256":"3261c088f3a93ce55c2191d68bf3deeec210176f1e552cabcb573d744f27b0d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3261c088f3a93ce55c2191d68bf3deeec210176f1e552cabcb573d744f27b0d7","first_computed_at":"2026-05-18T02:03:06.559147Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:06.559147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GkWyHF4dQVHo0HSp4MjPtW4tCj7cyeDIWWkz5TJLWdG7eW5tLySKodw/a0ID2CJnZGbrF0G5wcew5jF6gYS0BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:06.559671Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.4470","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92d18a0021c8150b1711d29d2c395ca6f33859a6fc86228dfd91db014d5b7c5b","sha256:6e0d48a1eba4dc9286f9cef092da55a19b9ee656cad4634fde50e5bb70838d5d"],"state_sha256":"91204c706c0410dee870ab59927021ddb862c3c1a80fcf806babb4eee6777b47"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DWT7y70OHgICXtAXwrSUWm3xYcao/9Y1KxatopjdyAvojikIg+pLEP5CLgH+VsHwyRhyeAbLUWVDAMuk6jyVBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T06:29:54.749359Z","bundle_sha256":"52f77718e560ff6460065cd29733444110ec82534ef0085a83f4cdfed5a9eb85"}}