{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:VGYPC5LOMM6PEQCX5DGVGITS2K","short_pith_number":"pith:VGYPC5LO","canonical_record":{"source":{"id":"1908.05579","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-15T15:14:56Z","cross_cats_sorted":[],"title_canon_sha256":"c86e83f447fb10f819855c7e731d5cf6585867ce8d213505791ac7c386d049e3","abstract_canon_sha256":"03bb293cbf3f1ab5b8ed376328b6fc4cdd2f8507308a13e7f1af3e78e8b83bbd"},"schema_version":"1.0"},"canonical_sha256":"a9b0f1756e633cf24057e8cd532272d2b89bc15b210501c672d39348a0300641","source":{"kind":"arxiv","id":"1908.05579","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.05579","created_at":"2026-07-05T03:57:22Z"},{"alias_kind":"arxiv_version","alias_value":"1908.05579v3","created_at":"2026-07-05T03:57:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05579","created_at":"2026-07-05T03:57:22Z"},{"alias_kind":"pith_short_12","alias_value":"VGYPC5LOMM6P","created_at":"2026-07-05T03:57:22Z"},{"alias_kind":"pith_short_16","alias_value":"VGYPC5LOMM6PEQCX","created_at":"2026-07-05T03:57:22Z"},{"alias_kind":"pith_short_8","alias_value":"VGYPC5LO","created_at":"2026-07-05T03:57:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:VGYPC5LOMM6PEQCX5DGVGITS2K","target":"record","payload":{"canonical_record":{"source":{"id":"1908.05579","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-15T15:14:56Z","cross_cats_sorted":[],"title_canon_sha256":"c86e83f447fb10f819855c7e731d5cf6585867ce8d213505791ac7c386d049e3","abstract_canon_sha256":"03bb293cbf3f1ab5b8ed376328b6fc4cdd2f8507308a13e7f1af3e78e8b83bbd"},"schema_version":"1.0"},"canonical_sha256":"a9b0f1756e633cf24057e8cd532272d2b89bc15b210501c672d39348a0300641","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:57:22.893959Z","signature_b64":"P7HMNTzOnVpjcnXnbMS2ssqfwps8UGw/7cKTH8N8QvyXR0K/khwOl8IvYx1ultCehZ5Jr8Z7oH2jc6/5iSAODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9b0f1756e633cf24057e8cd532272d2b89bc15b210501c672d39348a0300641","last_reissued_at":"2026-07-05T03:57:22.893593Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:57:22.893593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.05579","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:57:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nr9cXgxbwsA18v4zzbKbnbYAPMlIFKvZZjs5E9ZpwHfqBkN5wC6wc9Hlmy7BAl7Z9z00cb3pEXCbWtIzZGAjDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T06:32:55.714859Z"},"content_sha256":"59168b9e327e8b6b08dbf6fdb976569b32f797673fefeac66d710db6f9054626","schema_version":"1.0","event_id":"sha256:59168b9e327e8b6b08dbf6fdb976569b32f797673fefeac66d710db6f9054626"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:VGYPC5LOMM6PEQCX5DGVGITS2K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Frequently dense harmonic functions and universal martingales on trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Evgeny Abakumov, Massimo Picardello, Vassili Nestoridis","submitted_at":"2019-08-15T15:14:56Z","abstract_excerpt":"We prove the existence of harmonic functions $f$ on trees, with respect to suitable transient transition operators $P$, that satisfy an analogue of Menshov universal property in the following sense: $f$ is the Poisson transform of a martingale on the boundary of the tree (equipped with the harmonic measure $m$ induced by $P$) such that, for every measurable function $h$ on the boundary, it contains a subsequence that converges to $h$ in measure. Moreover, the martingale visits every open set of measurable functions with positive lower density."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05579","kind":"arxiv","version":3},"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/1908.05579/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":"2026-07-05T03:57:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z9pL7yfy667Oov1S1oidLh2XYWXjSjOmN9maMcru2oz5K9UUSIP1/tpESFtzlnZ9o//M0h9I8+ezYLdx8rQkBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T06:32:55.715558Z"},"content_sha256":"83260d592f7af4195ca90508459908959d8253dc90662cd65031676e77f9e92a","schema_version":"1.0","event_id":"sha256:83260d592f7af4195ca90508459908959d8253dc90662cd65031676e77f9e92a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VGYPC5LOMM6PEQCX5DGVGITS2K/bundle.json","state_url":"https://pith.science/pith/VGYPC5LOMM6PEQCX5DGVGITS2K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VGYPC5LOMM6PEQCX5DGVGITS2K/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":"2026-08-16T06:32:55Z","links":{"resolver":"https://pith.science/pith/VGYPC5LOMM6PEQCX5DGVGITS2K","bundle":"https://pith.science/pith/VGYPC5LOMM6PEQCX5DGVGITS2K/bundle.json","state":"https://pith.science/pith/VGYPC5LOMM6PEQCX5DGVGITS2K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VGYPC5LOMM6PEQCX5DGVGITS2K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VGYPC5LOMM6PEQCX5DGVGITS2K","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":"03bb293cbf3f1ab5b8ed376328b6fc4cdd2f8507308a13e7f1af3e78e8b83bbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-15T15:14:56Z","title_canon_sha256":"c86e83f447fb10f819855c7e731d5cf6585867ce8d213505791ac7c386d049e3"},"schema_version":"1.0","source":{"id":"1908.05579","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.05579","created_at":"2026-07-05T03:57:22Z"},{"alias_kind":"arxiv_version","alias_value":"1908.05579v3","created_at":"2026-07-05T03:57:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05579","created_at":"2026-07-05T03:57:22Z"},{"alias_kind":"pith_short_12","alias_value":"VGYPC5LOMM6P","created_at":"2026-07-05T03:57:22Z"},{"alias_kind":"pith_short_16","alias_value":"VGYPC5LOMM6PEQCX","created_at":"2026-07-05T03:57:22Z"},{"alias_kind":"pith_short_8","alias_value":"VGYPC5LO","created_at":"2026-07-05T03:57:22Z"}],"graph_snapshots":[{"event_id":"sha256:83260d592f7af4195ca90508459908959d8253dc90662cd65031676e77f9e92a","target":"graph","created_at":"2026-07-05T03:57:22Z","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/1908.05579/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove the existence of harmonic functions $f$ on trees, with respect to suitable transient transition operators $P$, that satisfy an analogue of Menshov universal property in the following sense: $f$ is the Poisson transform of a martingale on the boundary of the tree (equipped with the harmonic measure $m$ induced by $P$) such that, for every measurable function $h$ on the boundary, it contains a subsequence that converges to $h$ in measure. Moreover, the martingale visits every open set of measurable functions with positive lower density.","authors_text":"Evgeny Abakumov, Massimo Picardello, Vassili Nestoridis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-15T15:14:56Z","title":"Frequently dense harmonic functions and universal martingales on trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05579","kind":"arxiv","version":3},"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":"sha256:59168b9e327e8b6b08dbf6fdb976569b32f797673fefeac66d710db6f9054626","target":"record","created_at":"2026-07-05T03:57:22Z","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":"03bb293cbf3f1ab5b8ed376328b6fc4cdd2f8507308a13e7f1af3e78e8b83bbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-15T15:14:56Z","title_canon_sha256":"c86e83f447fb10f819855c7e731d5cf6585867ce8d213505791ac7c386d049e3"},"schema_version":"1.0","source":{"id":"1908.05579","kind":"arxiv","version":3}},"canonical_sha256":"a9b0f1756e633cf24057e8cd532272d2b89bc15b210501c672d39348a0300641","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9b0f1756e633cf24057e8cd532272d2b89bc15b210501c672d39348a0300641","first_computed_at":"2026-07-05T03:57:22.893593Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:57:22.893593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P7HMNTzOnVpjcnXnbMS2ssqfwps8UGw/7cKTH8N8QvyXR0K/khwOl8IvYx1ultCehZ5Jr8Z7oH2jc6/5iSAODA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:57:22.893959Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.05579","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59168b9e327e8b6b08dbf6fdb976569b32f797673fefeac66d710db6f9054626","sha256:83260d592f7af4195ca90508459908959d8253dc90662cd65031676e77f9e92a"],"state_sha256":"fcc96f5451851f80812b9f96a24ddf795ff35638df15e2dbd5fae1cdfa7ee1ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p+ALw91OLBUO3PvN8dWNF/f/z1vdgFNUOYB/LSeihLYGtm3NmItDAD65Ep2bPbSka2GPUTGbzfREQXu0y811AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T06:32:55.719618Z","bundle_sha256":"7e3f5aede1354f174470c1ec205dab69acdffe38f71861075f9cf47929da408e"}}