{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:BMUYLXLGQOOWC7NGEADDRBYDKR","short_pith_number":"pith:BMUYLXLG","canonical_record":{"source":{"id":"2111.14414","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-11-29T09:52:29Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"e087ae6b836c26820143b8e319b96ad356fb55e2a76a3caa9186fcbe287e5d51","abstract_canon_sha256":"10b1e3d44b0a39940912518d723b2ba613584c7eb914ca2b0c996697b7dee80b"},"schema_version":"1.0"},"canonical_sha256":"0b2985dd66839d617da620063887035459024402220c0354d4f2cbe102db631b","source":{"kind":"arxiv","id":"2111.14414","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.14414","created_at":"2026-07-05T03:35:51Z"},{"alias_kind":"arxiv_version","alias_value":"2111.14414v1","created_at":"2026-07-05T03:35:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.14414","created_at":"2026-07-05T03:35:51Z"},{"alias_kind":"pith_short_12","alias_value":"BMUYLXLGQOOW","created_at":"2026-07-05T03:35:51Z"},{"alias_kind":"pith_short_16","alias_value":"BMUYLXLGQOOWC7NG","created_at":"2026-07-05T03:35:51Z"},{"alias_kind":"pith_short_8","alias_value":"BMUYLXLG","created_at":"2026-07-05T03:35:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:BMUYLXLGQOOWC7NGEADDRBYDKR","target":"record","payload":{"canonical_record":{"source":{"id":"2111.14414","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-11-29T09:52:29Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"e087ae6b836c26820143b8e319b96ad356fb55e2a76a3caa9186fcbe287e5d51","abstract_canon_sha256":"10b1e3d44b0a39940912518d723b2ba613584c7eb914ca2b0c996697b7dee80b"},"schema_version":"1.0"},"canonical_sha256":"0b2985dd66839d617da620063887035459024402220c0354d4f2cbe102db631b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:35:51.579536Z","signature_b64":"F4NFgKBWuD2ZmuwCdJQD88H713+T9NskQTcqQY9EMKIPJ3De/izEUPSFJTGImLUUsROeHabGQtlNUHV6lplMCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b2985dd66839d617da620063887035459024402220c0354d4f2cbe102db631b","last_reissued_at":"2026-07-05T03:35:51.579098Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:35:51.579098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2111.14414","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":"2026-07-05T03:35:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8sEai1mOkHQtCVzlOLUzo0IFy8hA62GW2lls+hstG6m9NjxL/qksyPydB5/pN/UJzxzYkGRZDP++0cSeKDRhDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T13:33:54.478377Z"},"content_sha256":"2624a313457b4f42667781bef953ac5fe8b4bd8dfae9c713883210516ced032e","schema_version":"1.0","event_id":"sha256:2624a313457b4f42667781bef953ac5fe8b4bd8dfae9c713883210516ced032e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:BMUYLXLGQOOWC7NGEADDRBYDKR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Near critical scaling relations for planar Bernoulli percolation without differential inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Hugo Duminil-Copin, Ioan Manolescu, Vincent Tassion","submitted_at":"2021-11-29T09:52:29Z","abstract_excerpt":"We provide a new proof of the near-critical scaling relation $\\beta=\\xi_1\\nu$ for Bernoulli percolation on the square lattice already proved by Kesten in 1987. We rely on a novel approach that does not invoke Russo's formula, but rather relates differences in crossing probabilities at different scales. The argument is shorter and more robust than previous ones and is more likely to be adapted to other models. The same approach may be used to prove the other scaling relations appearing in Kesten's work."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.14414","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2111.14414/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:35:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aQr3VdujhEMZw5hXdMIVkImmVQgW/UHdTEfzHK250UJIZvAmL0moDDiVx0KeHDt4u68xu0P9O/ZHO71XlxP3CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T13:33:54.479110Z"},"content_sha256":"3ac173f60bb3d66ba4a6b7a32c427dd934b60d5ae92321079488543534dee0ee","schema_version":"1.0","event_id":"sha256:3ac173f60bb3d66ba4a6b7a32c427dd934b60d5ae92321079488543534dee0ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BMUYLXLGQOOWC7NGEADDRBYDKR/bundle.json","state_url":"https://pith.science/pith/BMUYLXLGQOOWC7NGEADDRBYDKR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BMUYLXLGQOOWC7NGEADDRBYDKR/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":"2026-08-12T13:33:54Z","links":{"resolver":"https://pith.science/pith/BMUYLXLGQOOWC7NGEADDRBYDKR","bundle":"https://pith.science/pith/BMUYLXLGQOOWC7NGEADDRBYDKR/bundle.json","state":"https://pith.science/pith/BMUYLXLGQOOWC7NGEADDRBYDKR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BMUYLXLGQOOWC7NGEADDRBYDKR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:BMUYLXLGQOOWC7NGEADDRBYDKR","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":"10b1e3d44b0a39940912518d723b2ba613584c7eb914ca2b0c996697b7dee80b","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-11-29T09:52:29Z","title_canon_sha256":"e087ae6b836c26820143b8e319b96ad356fb55e2a76a3caa9186fcbe287e5d51"},"schema_version":"1.0","source":{"id":"2111.14414","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.14414","created_at":"2026-07-05T03:35:51Z"},{"alias_kind":"arxiv_version","alias_value":"2111.14414v1","created_at":"2026-07-05T03:35:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.14414","created_at":"2026-07-05T03:35:51Z"},{"alias_kind":"pith_short_12","alias_value":"BMUYLXLGQOOW","created_at":"2026-07-05T03:35:51Z"},{"alias_kind":"pith_short_16","alias_value":"BMUYLXLGQOOWC7NG","created_at":"2026-07-05T03:35:51Z"},{"alias_kind":"pith_short_8","alias_value":"BMUYLXLG","created_at":"2026-07-05T03:35:51Z"}],"graph_snapshots":[{"event_id":"sha256:3ac173f60bb3d66ba4a6b7a32c427dd934b60d5ae92321079488543534dee0ee","target":"graph","created_at":"2026-07-05T03:35:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2111.14414/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide a new proof of the near-critical scaling relation $\\beta=\\xi_1\\nu$ for Bernoulli percolation on the square lattice already proved by Kesten in 1987. We rely on a novel approach that does not invoke Russo's formula, but rather relates differences in crossing probabilities at different scales. The argument is shorter and more robust than previous ones and is more likely to be adapted to other models. The same approach may be used to prove the other scaling relations appearing in Kesten's work.","authors_text":"Hugo Duminil-Copin, Ioan Manolescu, Vincent Tassion","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-11-29T09:52:29Z","title":"Near critical scaling relations for planar Bernoulli percolation without differential inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.14414","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":"sha256:2624a313457b4f42667781bef953ac5fe8b4bd8dfae9c713883210516ced032e","target":"record","created_at":"2026-07-05T03:35:51Z","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":"10b1e3d44b0a39940912518d723b2ba613584c7eb914ca2b0c996697b7dee80b","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-11-29T09:52:29Z","title_canon_sha256":"e087ae6b836c26820143b8e319b96ad356fb55e2a76a3caa9186fcbe287e5d51"},"schema_version":"1.0","source":{"id":"2111.14414","kind":"arxiv","version":1}},"canonical_sha256":"0b2985dd66839d617da620063887035459024402220c0354d4f2cbe102db631b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b2985dd66839d617da620063887035459024402220c0354d4f2cbe102db631b","first_computed_at":"2026-07-05T03:35:51.579098Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:35:51.579098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F4NFgKBWuD2ZmuwCdJQD88H713+T9NskQTcqQY9EMKIPJ3De/izEUPSFJTGImLUUsROeHabGQtlNUHV6lplMCg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:35:51.579536Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.14414","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2624a313457b4f42667781bef953ac5fe8b4bd8dfae9c713883210516ced032e","sha256:3ac173f60bb3d66ba4a6b7a32c427dd934b60d5ae92321079488543534dee0ee"],"state_sha256":"a1c2346c712c343b81fa43a6f2afd57edc0316dc145244a71d686c85f7985bfe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g/Vd8fkk2AYCkcYAH9j/3vm5FaQqb7i6DkEcdhprNqj8I9ysYKWNlaK9FsGI2Q9iInWBZ54mSlpF7yn6bRxpAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T13:33:54.486158Z","bundle_sha256":"edebbe7b38aa10ccfff937c27a6e66ce2f440719bb00e39349a8176ea25da68e"}}