{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:HVVX6SR54KY3VX5ATDDDTOQ575","short_pith_number":"pith:HVVX6SR5","canonical_record":{"source":{"id":"2107.05322","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.NI","submitted_at":"2021-07-12T11:19:31Z","cross_cats_sorted":[],"title_canon_sha256":"c3abfc3aecb5341261343d169d9a4db31b5c87942950817e4a9851a93e983b2e","abstract_canon_sha256":"1f8b670d59505d14f27963a0bc2708b9537498c1e21939c2d07a56f9c83c38ee"},"schema_version":"1.0"},"canonical_sha256":"3d6b7f4a3de2b1badfa098c639ba1dff464a3c46abb5babfd017d6f726555f52","source":{"kind":"arxiv","id":"2107.05322","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.05322","created_at":"2026-07-05T02:57:01Z"},{"alias_kind":"arxiv_version","alias_value":"2107.05322v1","created_at":"2026-07-05T02:57:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.05322","created_at":"2026-07-05T02:57:01Z"},{"alias_kind":"pith_short_12","alias_value":"HVVX6SR54KY3","created_at":"2026-07-05T02:57:01Z"},{"alias_kind":"pith_short_16","alias_value":"HVVX6SR54KY3VX5A","created_at":"2026-07-05T02:57:01Z"},{"alias_kind":"pith_short_8","alias_value":"HVVX6SR5","created_at":"2026-07-05T02:57:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:HVVX6SR54KY3VX5ATDDDTOQ575","target":"record","payload":{"canonical_record":{"source":{"id":"2107.05322","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.NI","submitted_at":"2021-07-12T11:19:31Z","cross_cats_sorted":[],"title_canon_sha256":"c3abfc3aecb5341261343d169d9a4db31b5c87942950817e4a9851a93e983b2e","abstract_canon_sha256":"1f8b670d59505d14f27963a0bc2708b9537498c1e21939c2d07a56f9c83c38ee"},"schema_version":"1.0"},"canonical_sha256":"3d6b7f4a3de2b1badfa098c639ba1dff464a3c46abb5babfd017d6f726555f52","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:57:01.589486Z","signature_b64":"0kXLoU6Ue2xlEqKZWXtVC0iA8j7wQbA4TCCLwyxV/ImAvhvmbMbOnFTK0q77rn62d0TRw/Ry/F1g36BFHewJCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d6b7f4a3de2b1badfa098c639ba1dff464a3c46abb5babfd017d6f726555f52","last_reissued_at":"2026-07-05T02:57:01.589071Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:57:01.589071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2107.05322","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":"2026-07-05T02:57:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wL6jHuENbZiD26ebubLL4YNlxSFOTXb9qXW46KePEiAgq7H4vUXlUn1APUdg35Fzxt8NZasBsYk2Enb6UobEBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T08:05:26.281012Z"},"content_sha256":"64b2050bad115b4097b82829f5fb550a869458478a1fe6b350ed8ba7200bde55","schema_version":"1.0","event_id":"sha256:64b2050bad115b4097b82829f5fb550a869458478a1fe6b350ed8ba7200bde55"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:HVVX6SR54KY3VX5ATDDDTOQ575","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimally Reliable & Cheap Payment Flows on the Lightning Network","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.NI","authors_text":"Rene Pickhardt, Stefan Richter","submitted_at":"2021-07-12T11:19:31Z","abstract_excerpt":"Today, payment paths in Bitcoin's Lightning Network are found by searching for shortest paths on the fee graph. We enhance this approach in two dimensions. Firstly, we take into account the probability of a payment actually being possible due to the unknown balance distributions in the channels. Secondly, we use minimum cost flows as a proper generalization of shortest paths to multi-part payments (MPP). In particular we show that under plausible assumptions about the balance distributions we can find the most likely MPP for any given set of senders, recipients and amounts by solving for a (ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.05322","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/2107.05322/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":"2026-07-05T02:57:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZnUEyAkAnLCI1t705tyHFqLIW2f1gogEBOgwaHChCVpKDNNV9rEKyPUuD5e3SPJ8/AOxbbieIWRR4DPecDX8Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T08:05:26.281502Z"},"content_sha256":"9d57aee090aa285aafa6ae9ec2d1ddd3c9deb0f5f28187c4e7e6a228639b54bf","schema_version":"1.0","event_id":"sha256:9d57aee090aa285aafa6ae9ec2d1ddd3c9deb0f5f28187c4e7e6a228639b54bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HVVX6SR54KY3VX5ATDDDTOQ575/bundle.json","state_url":"https://pith.science/pith/HVVX6SR54KY3VX5ATDDDTOQ575/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HVVX6SR54KY3VX5ATDDDTOQ575/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":"2026-08-04T08:05:26Z","links":{"resolver":"https://pith.science/pith/HVVX6SR54KY3VX5ATDDDTOQ575","bundle":"https://pith.science/pith/HVVX6SR54KY3VX5ATDDDTOQ575/bundle.json","state":"https://pith.science/pith/HVVX6SR54KY3VX5ATDDDTOQ575/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HVVX6SR54KY3VX5ATDDDTOQ575/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:HVVX6SR54KY3VX5ATDDDTOQ575","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":"1f8b670d59505d14f27963a0bc2708b9537498c1e21939c2d07a56f9c83c38ee","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.NI","submitted_at":"2021-07-12T11:19:31Z","title_canon_sha256":"c3abfc3aecb5341261343d169d9a4db31b5c87942950817e4a9851a93e983b2e"},"schema_version":"1.0","source":{"id":"2107.05322","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.05322","created_at":"2026-07-05T02:57:01Z"},{"alias_kind":"arxiv_version","alias_value":"2107.05322v1","created_at":"2026-07-05T02:57:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.05322","created_at":"2026-07-05T02:57:01Z"},{"alias_kind":"pith_short_12","alias_value":"HVVX6SR54KY3","created_at":"2026-07-05T02:57:01Z"},{"alias_kind":"pith_short_16","alias_value":"HVVX6SR54KY3VX5A","created_at":"2026-07-05T02:57:01Z"},{"alias_kind":"pith_short_8","alias_value":"HVVX6SR5","created_at":"2026-07-05T02:57:01Z"}],"graph_snapshots":[{"event_id":"sha256:9d57aee090aa285aafa6ae9ec2d1ddd3c9deb0f5f28187c4e7e6a228639b54bf","target":"graph","created_at":"2026-07-05T02:57:01Z","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/2107.05322/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Today, payment paths in Bitcoin's Lightning Network are found by searching for shortest paths on the fee graph. We enhance this approach in two dimensions. Firstly, we take into account the probability of a payment actually being possible due to the unknown balance distributions in the channels. Secondly, we use minimum cost flows as a proper generalization of shortest paths to multi-part payments (MPP). In particular we show that under plausible assumptions about the balance distributions we can find the most likely MPP for any given set of senders, recipients and amounts by solving for a (ge","authors_text":"Rene Pickhardt, Stefan Richter","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.NI","submitted_at":"2021-07-12T11:19:31Z","title":"Optimally Reliable & Cheap Payment Flows on the Lightning Network"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.05322","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":"sha256:64b2050bad115b4097b82829f5fb550a869458478a1fe6b350ed8ba7200bde55","target":"record","created_at":"2026-07-05T02:57:01Z","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":"1f8b670d59505d14f27963a0bc2708b9537498c1e21939c2d07a56f9c83c38ee","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.NI","submitted_at":"2021-07-12T11:19:31Z","title_canon_sha256":"c3abfc3aecb5341261343d169d9a4db31b5c87942950817e4a9851a93e983b2e"},"schema_version":"1.0","source":{"id":"2107.05322","kind":"arxiv","version":1}},"canonical_sha256":"3d6b7f4a3de2b1badfa098c639ba1dff464a3c46abb5babfd017d6f726555f52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d6b7f4a3de2b1badfa098c639ba1dff464a3c46abb5babfd017d6f726555f52","first_computed_at":"2026-07-05T02:57:01.589071Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:57:01.589071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0kXLoU6Ue2xlEqKZWXtVC0iA8j7wQbA4TCCLwyxV/ImAvhvmbMbOnFTK0q77rn62d0TRw/Ry/F1g36BFHewJCg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:57:01.589486Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.05322","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64b2050bad115b4097b82829f5fb550a869458478a1fe6b350ed8ba7200bde55","sha256:9d57aee090aa285aafa6ae9ec2d1ddd3c9deb0f5f28187c4e7e6a228639b54bf"],"state_sha256":"118438636bf5353ce0663c341b4216582ea5c3758d1f55181a0124f54c41db61"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"djtZS1qjj20ujbFeckaJeQaYj2V+JFAIG8kmzABp9iTpzd0OyrKhwFp8XTK0zqcSBKnNqYW1F2PQ2Cd8LqaRDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T08:05:26.286862Z","bundle_sha256":"a09ab36b3bab944990a920f2b28310896f84664d39e25c5138193965ab2d7221"}}