{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:3BW3VATPX2NIAISOF6J2S24IN3","short_pith_number":"pith:3BW3VATP","canonical_record":{"source":{"id":"2606.17792","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-16T11:11:54Z","cross_cats_sorted":[],"title_canon_sha256":"a18b7788918c63499789f0e15d09895876ba1cf2813d5901ff0dee583e55cab9","abstract_canon_sha256":"384d2e8c81cceea140c9037807a2c347b4d883ad36c54a8654a18eb66f4f22c5"},"schema_version":"1.0"},"canonical_sha256":"d86dba826fbe9a80224e2f93a96b886edb92155404f2511345f8ed0caecb7bfa","source":{"kind":"arxiv","id":"2606.17792","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.17792","created_at":"2026-06-19T16:10:21Z"},{"alias_kind":"arxiv_version","alias_value":"2606.17792v1","created_at":"2026-06-19T16:10:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.17792","created_at":"2026-06-19T16:10:21Z"},{"alias_kind":"pith_short_12","alias_value":"3BW3VATPX2NI","created_at":"2026-06-19T16:10:21Z"},{"alias_kind":"pith_short_16","alias_value":"3BW3VATPX2NIAISO","created_at":"2026-06-19T16:10:21Z"},{"alias_kind":"pith_short_8","alias_value":"3BW3VATP","created_at":"2026-06-19T16:10:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:3BW3VATPX2NIAISOF6J2S24IN3","target":"record","payload":{"canonical_record":{"source":{"id":"2606.17792","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-16T11:11:54Z","cross_cats_sorted":[],"title_canon_sha256":"a18b7788918c63499789f0e15d09895876ba1cf2813d5901ff0dee583e55cab9","abstract_canon_sha256":"384d2e8c81cceea140c9037807a2c347b4d883ad36c54a8654a18eb66f4f22c5"},"schema_version":"1.0"},"canonical_sha256":"d86dba826fbe9a80224e2f93a96b886edb92155404f2511345f8ed0caecb7bfa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:21.877713Z","signature_b64":"BPdmbwp16y6ALXQ7NPDdyukfqz9LPWsbjgVpcotyU1Vr02NsBODxDufqEP2GSnwy5g95fEZ5zCLUN2ITF3NmCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d86dba826fbe9a80224e2f93a96b886edb92155404f2511345f8ed0caecb7bfa","last_reissued_at":"2026-06-19T16:10:21.877297Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:21.877297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.17792","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":"2026-06-19T16:10:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9ePT/4UbkfIVkONf45ooX34WAWu19kDhdHLZylgsD/QM4iNiS3RRTCsFUot0vXurf1VgA7yhLV6eeeIE1FkZCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T15:24:46.986730Z"},"content_sha256":"f2457c314cf38cf0bead09aa6e92979b03ed48d543481623e4cca64d107620a7","schema_version":"1.0","event_id":"sha256:f2457c314cf38cf0bead09aa6e92979b03ed48d543481623e4cca64d107620a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:3BW3VATPX2NIAISOF6J2S24IN3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Loss of Tension in an Infinite Membrane with Holes of Decaying Spatial Density","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lukas Early, Stanislav Volkov","submitted_at":"2026-06-16T11:11:54Z","abstract_excerpt":"What is the effect of randomly removing material from an infinite stretched membrane? Under what conditions can the membrane still sustain tension? This problem was introduced by Robert Connelly in connection with applications of rigidity theory in the natural sciences, and was later studied in M. V. Menshikov, K. A. Rybnikov, and S. E. Volkov, \"The loss of tension in an infinite membrane with holes distributed according to a Poisson law\" (2002); a discrete version was also considered in Robert Connelly, Konstantin Rybnikov, and Stanislav Volkov, \"Percolation and the Loss of Tension in an Infi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17792","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/2606.17792/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":"2026-06-19T16:10:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gpsA8frEggYEQUbovFgL90l6ZcpQnPtshdiFGEd6xwkQPV0IaaQ8eIPngRlwN7JYCM4WJK9+c2YAA4zmfcwzBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T15:24:46.987116Z"},"content_sha256":"04d3af4a7aa0df52513579e5f129d84cc61effd4450bb9e665b7fdb5e834a124","schema_version":"1.0","event_id":"sha256:04d3af4a7aa0df52513579e5f129d84cc61effd4450bb9e665b7fdb5e834a124"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3BW3VATPX2NIAISOF6J2S24IN3/bundle.json","state_url":"https://pith.science/pith/3BW3VATPX2NIAISOF6J2S24IN3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3BW3VATPX2NIAISOF6J2S24IN3/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":"2026-06-22T15:24:46Z","links":{"resolver":"https://pith.science/pith/3BW3VATPX2NIAISOF6J2S24IN3","bundle":"https://pith.science/pith/3BW3VATPX2NIAISOF6J2S24IN3/bundle.json","state":"https://pith.science/pith/3BW3VATPX2NIAISOF6J2S24IN3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3BW3VATPX2NIAISOF6J2S24IN3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3BW3VATPX2NIAISOF6J2S24IN3","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":"384d2e8c81cceea140c9037807a2c347b4d883ad36c54a8654a18eb66f4f22c5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-16T11:11:54Z","title_canon_sha256":"a18b7788918c63499789f0e15d09895876ba1cf2813d5901ff0dee583e55cab9"},"schema_version":"1.0","source":{"id":"2606.17792","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.17792","created_at":"2026-06-19T16:10:21Z"},{"alias_kind":"arxiv_version","alias_value":"2606.17792v1","created_at":"2026-06-19T16:10:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.17792","created_at":"2026-06-19T16:10:21Z"},{"alias_kind":"pith_short_12","alias_value":"3BW3VATPX2NI","created_at":"2026-06-19T16:10:21Z"},{"alias_kind":"pith_short_16","alias_value":"3BW3VATPX2NIAISO","created_at":"2026-06-19T16:10:21Z"},{"alias_kind":"pith_short_8","alias_value":"3BW3VATP","created_at":"2026-06-19T16:10:21Z"}],"graph_snapshots":[{"event_id":"sha256:04d3af4a7aa0df52513579e5f129d84cc61effd4450bb9e665b7fdb5e834a124","target":"graph","created_at":"2026-06-19T16:10:21Z","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/2606.17792/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"What is the effect of randomly removing material from an infinite stretched membrane? Under what conditions can the membrane still sustain tension? This problem was introduced by Robert Connelly in connection with applications of rigidity theory in the natural sciences, and was later studied in M. V. Menshikov, K. A. Rybnikov, and S. E. Volkov, \"The loss of tension in an infinite membrane with holes distributed according to a Poisson law\" (2002); a discrete version was also considered in Robert Connelly, Konstantin Rybnikov, and Stanislav Volkov, \"Percolation and the Loss of Tension in an Infi","authors_text":"Lukas Early, Stanislav Volkov","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-16T11:11:54Z","title":"The Loss of Tension in an Infinite Membrane with Holes of Decaying Spatial Density"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17792","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:f2457c314cf38cf0bead09aa6e92979b03ed48d543481623e4cca64d107620a7","target":"record","created_at":"2026-06-19T16:10:21Z","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":"384d2e8c81cceea140c9037807a2c347b4d883ad36c54a8654a18eb66f4f22c5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-16T11:11:54Z","title_canon_sha256":"a18b7788918c63499789f0e15d09895876ba1cf2813d5901ff0dee583e55cab9"},"schema_version":"1.0","source":{"id":"2606.17792","kind":"arxiv","version":1}},"canonical_sha256":"d86dba826fbe9a80224e2f93a96b886edb92155404f2511345f8ed0caecb7bfa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d86dba826fbe9a80224e2f93a96b886edb92155404f2511345f8ed0caecb7bfa","first_computed_at":"2026-06-19T16:10:21.877297Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:21.877297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BPdmbwp16y6ALXQ7NPDdyukfqz9LPWsbjgVpcotyU1Vr02NsBODxDufqEP2GSnwy5g95fEZ5zCLUN2ITF3NmCw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:21.877713Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.17792","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2457c314cf38cf0bead09aa6e92979b03ed48d543481623e4cca64d107620a7","sha256:04d3af4a7aa0df52513579e5f129d84cc61effd4450bb9e665b7fdb5e834a124"],"state_sha256":"7422d57babccec684d614e58470a809987873333306612a17dbc86e6ed310024"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KFOM48bLyiYI0rXQ7boJsB/27tYwtefbJqlArCqSHHjVb3JK2UMAUBgXvdIG0r8sur4AK3wPICoLZi4MRcsTBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T15:24:46.989225Z","bundle_sha256":"3a7896311cf732e2d998800e7ef3fbd3e04c7d3e2be221d9752e3abb64055d0a"}}