{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:3QWL454WS7D2YHMVKTMPST73B6","short_pith_number":"pith:3QWL454W","canonical_record":{"source":{"id":"1610.00021","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-30T20:13:17Z","cross_cats_sorted":[],"title_canon_sha256":"01d5c6826f94a16cd9a7f5726fb75270055bca565f7f4ec39a5f95f3bc8e8f2d","abstract_canon_sha256":"fdc9c38215aa52d67d09e0ed36ebc1f86e6195eeaf3ddc2427958050153d361d"},"schema_version":"1.0"},"canonical_sha256":"dc2cbe779697c7ac1d9554d8f94ffb0faaa76a0d43c96938fe57853143bc153f","source":{"kind":"arxiv","id":"1610.00021","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.00021","created_at":"2026-05-18T00:20:32Z"},{"alias_kind":"arxiv_version","alias_value":"1610.00021v2","created_at":"2026-05-18T00:20:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00021","created_at":"2026-05-18T00:20:32Z"},{"alias_kind":"pith_short_12","alias_value":"3QWL454WS7D2","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3QWL454WS7D2YHMV","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3QWL454W","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:3QWL454WS7D2YHMVKTMPST73B6","target":"record","payload":{"canonical_record":{"source":{"id":"1610.00021","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-30T20:13:17Z","cross_cats_sorted":[],"title_canon_sha256":"01d5c6826f94a16cd9a7f5726fb75270055bca565f7f4ec39a5f95f3bc8e8f2d","abstract_canon_sha256":"fdc9c38215aa52d67d09e0ed36ebc1f86e6195eeaf3ddc2427958050153d361d"},"schema_version":"1.0"},"canonical_sha256":"dc2cbe779697c7ac1d9554d8f94ffb0faaa76a0d43c96938fe57853143bc153f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:32.492216Z","signature_b64":"ZFE4GImRgXg2Di8IA2A2yDFoIqsn7NURY7WXlr8bolbU2MrZfyxGsGJaIj1LDNvNuSHsFc3v6yh5nd2lsZwuAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc2cbe779697c7ac1d9554d8f94ffb0faaa76a0d43c96938fe57853143bc153f","last_reissued_at":"2026-05-18T00:20:32.491643Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:32.491643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.00021","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dn41HatXvBdHgpoCnfzfBnGscOOztH69P7jq0iCKLXthYbIsudYAiU7erJiw683rq8uAi4NTG4AlPWWvhY3mDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T05:45:24.007786Z"},"content_sha256":"894586eb8aaaa729de827d62e762ea06cfd5a38ea080d38e7d1d9b70f12c00f9","schema_version":"1.0","event_id":"sha256:894586eb8aaaa729de827d62e762ea06cfd5a38ea080d38e7d1d9b70f12c00f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:3QWL454WS7D2YHMVKTMPST73B6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Feller property of the multiplicative coalescent with linear deletion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Balazs Rath","submitted_at":"2016-09-30T20:13:17Z","abstract_excerpt":"We modify the definition of Aldous' multiplicative coalescent process and introduce the multiplicative coalescent with linear deletion (MCLD). A state of this process is a square-summable decreasing sequence of cluster sizes. Pairs of clusters merge with a rate equal to the product of their sizes and clusters are deleted with a rate linearly proportional to their size. We prove that the MCLD is a Feller process. This result is a key ingredient in the description of scaling limits of the evolution of component sizes of the mean field frozen percolation model and the so-called rigid representati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00021","kind":"arxiv","version":2},"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":"2026-05-18T00:20:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yq6nssGeWdnh6MCdbNnf1lIcARs9kI2aZV0osNdt0LpihwCXfHj/eHaquO+ygYrI1qJjEHw4BFvqkz1AVxCPAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T05:45:24.008476Z"},"content_sha256":"bfd186ee3430a6475de4b9c138cd92c0888efb76d6710494ea20d130925be6d8","schema_version":"1.0","event_id":"sha256:bfd186ee3430a6475de4b9c138cd92c0888efb76d6710494ea20d130925be6d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3QWL454WS7D2YHMVKTMPST73B6/bundle.json","state_url":"https://pith.science/pith/3QWL454WS7D2YHMVKTMPST73B6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3QWL454WS7D2YHMVKTMPST73B6/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":"2026-06-05T05:45:24Z","links":{"resolver":"https://pith.science/pith/3QWL454WS7D2YHMVKTMPST73B6","bundle":"https://pith.science/pith/3QWL454WS7D2YHMVKTMPST73B6/bundle.json","state":"https://pith.science/pith/3QWL454WS7D2YHMVKTMPST73B6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3QWL454WS7D2YHMVKTMPST73B6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3QWL454WS7D2YHMVKTMPST73B6","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":"fdc9c38215aa52d67d09e0ed36ebc1f86e6195eeaf3ddc2427958050153d361d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-30T20:13:17Z","title_canon_sha256":"01d5c6826f94a16cd9a7f5726fb75270055bca565f7f4ec39a5f95f3bc8e8f2d"},"schema_version":"1.0","source":{"id":"1610.00021","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.00021","created_at":"2026-05-18T00:20:32Z"},{"alias_kind":"arxiv_version","alias_value":"1610.00021v2","created_at":"2026-05-18T00:20:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00021","created_at":"2026-05-18T00:20:32Z"},{"alias_kind":"pith_short_12","alias_value":"3QWL454WS7D2","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3QWL454WS7D2YHMV","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3QWL454W","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:bfd186ee3430a6475de4b9c138cd92c0888efb76d6710494ea20d130925be6d8","target":"graph","created_at":"2026-05-18T00:20:32Z","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 modify the definition of Aldous' multiplicative coalescent process and introduce the multiplicative coalescent with linear deletion (MCLD). A state of this process is a square-summable decreasing sequence of cluster sizes. Pairs of clusters merge with a rate equal to the product of their sizes and clusters are deleted with a rate linearly proportional to their size. We prove that the MCLD is a Feller process. This result is a key ingredient in the description of scaling limits of the evolution of component sizes of the mean field frozen percolation model and the so-called rigid representati","authors_text":"Balazs Rath","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-30T20:13:17Z","title":"Feller property of the multiplicative coalescent with linear deletion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00021","kind":"arxiv","version":2},"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":"sha256:894586eb8aaaa729de827d62e762ea06cfd5a38ea080d38e7d1d9b70f12c00f9","target":"record","created_at":"2026-05-18T00:20:32Z","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":"fdc9c38215aa52d67d09e0ed36ebc1f86e6195eeaf3ddc2427958050153d361d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-30T20:13:17Z","title_canon_sha256":"01d5c6826f94a16cd9a7f5726fb75270055bca565f7f4ec39a5f95f3bc8e8f2d"},"schema_version":"1.0","source":{"id":"1610.00021","kind":"arxiv","version":2}},"canonical_sha256":"dc2cbe779697c7ac1d9554d8f94ffb0faaa76a0d43c96938fe57853143bc153f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc2cbe779697c7ac1d9554d8f94ffb0faaa76a0d43c96938fe57853143bc153f","first_computed_at":"2026-05-18T00:20:32.491643Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:32.491643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZFE4GImRgXg2Di8IA2A2yDFoIqsn7NURY7WXlr8bolbU2MrZfyxGsGJaIj1LDNvNuSHsFc3v6yh5nd2lsZwuAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:32.492216Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.00021","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:894586eb8aaaa729de827d62e762ea06cfd5a38ea080d38e7d1d9b70f12c00f9","sha256:bfd186ee3430a6475de4b9c138cd92c0888efb76d6710494ea20d130925be6d8"],"state_sha256":"f26cdf769e61de429175246e355172270531f667ac983dae62ad171c3f8c4127"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JjRK9b4QFCsNeawHTY7QWbsRIKGifCgJFxIKzXqkDO5ZFGcKPKt2EQH2hgmNlLg8gH/e72BCseJarqECSWhOBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T05:45:24.012018Z","bundle_sha256":"fc4589143043f9bb7da32c1fc194fd10824d0b45856dd2f89f3fac728755905e"}}