{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5377NQD547C7SYTKAWIVTACPR5","short_pith_number":"pith:5377NQD5","canonical_record":{"source":{"id":"1707.01984","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-06T22:27:38Z","cross_cats_sorted":["math-ph","math.AP","math.DS","math.MP"],"title_canon_sha256":"b0351d80ddc27f6022b8dd5fc05fb5174abe718fbe041b0f85e46be7d84c9295","abstract_canon_sha256":"7289dce2e88c8aca593dd5ae8f968c296281a4c9b99df7033853201e997be23f"},"schema_version":"1.0"},"canonical_sha256":"eefff6c07de7c5f9626a059159804f8f620075e2c9a10038d9f6d6a2bf4859cb","source":{"kind":"arxiv","id":"1707.01984","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01984","created_at":"2026-05-18T00:08:23Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01984v3","created_at":"2026-05-18T00:08:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01984","created_at":"2026-05-18T00:08:23Z"},{"alias_kind":"pith_short_12","alias_value":"5377NQD547C7","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5377NQD547C7SYTK","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5377NQD5","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5377NQD547C7SYTKAWIVTACPR5","target":"record","payload":{"canonical_record":{"source":{"id":"1707.01984","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-06T22:27:38Z","cross_cats_sorted":["math-ph","math.AP","math.DS","math.MP"],"title_canon_sha256":"b0351d80ddc27f6022b8dd5fc05fb5174abe718fbe041b0f85e46be7d84c9295","abstract_canon_sha256":"7289dce2e88c8aca593dd5ae8f968c296281a4c9b99df7033853201e997be23f"},"schema_version":"1.0"},"canonical_sha256":"eefff6c07de7c5f9626a059159804f8f620075e2c9a10038d9f6d6a2bf4859cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:23.617039Z","signature_b64":"s9P1DO+6W25xLsF+4rglncyoVIWRgSI+dX+8TIct5q3evAw9q5fbrCyJHZFAHnB8O8qQ+kc1c/GnoeImRhg/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eefff6c07de7c5f9626a059159804f8f620075e2c9a10038d9f6d6a2bf4859cb","last_reissued_at":"2026-05-18T00:08:23.616610Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:23.616610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.01984","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":"2026-05-18T00:08:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6cDzzDSHRPXVJdXjQuR60I9M3MYRAT8dNiE3oGoNmflGBm3qgQMkrNdWyuGPMzPKTo9fV4G5ygv8oLRk2ugSDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:30:26.569853Z"},"content_sha256":"99c86cfc09cef36ecbb8f45d6f719b88fc9e772a663be293c58000c648a8a934","schema_version":"1.0","event_id":"sha256:99c86cfc09cef36ecbb8f45d6f719b88fc9e772a663be293c58000c648a8a934"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5377NQD547C7SYTKAWIVTACPR5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamical pruning of rooted trees with applications to 1D ballistic annihilation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.DS","math.MP"],"primary_cat":"math.PR","authors_text":"Ilya Zaliapin, Yevgeniy Kovchegov","submitted_at":"2017-07-06T22:27:38Z","abstract_excerpt":"We introduce generalized dynamical pruning on rooted binary trees with edge lengths. The pruning removes parts of a tree $T$, starting from the leaves, according to a pruning function defined on subtrees within $T$. The generalized pruning encompasses a number of discrete and continuous pruning operations, including the tree erasure and Horton pruning. The main result is invariance of a finite critical binary Galton-Watson tree with exponential edge lengths with respect to the generalized dynamical pruning for an arbitrary admissible pruning function. The second part of the paper examines the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01984","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":""},"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":"2026-05-18T00:08:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kww4yRyMCj8yaGB7tujY3b4OMKzV/TWc4wvCU4T6rxB8hSoz9kprhHhZZoHDtAYTZzH5lODWVyH1H2i8aDdsBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:30:26.570200Z"},"content_sha256":"3f8df221082cd9c30b14ef3d081195b27f12b01f110aa2f2e6694fa27719a42f","schema_version":"1.0","event_id":"sha256:3f8df221082cd9c30b14ef3d081195b27f12b01f110aa2f2e6694fa27719a42f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5377NQD547C7SYTKAWIVTACPR5/bundle.json","state_url":"https://pith.science/pith/5377NQD547C7SYTKAWIVTACPR5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5377NQD547C7SYTKAWIVTACPR5/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":"2026-06-03T06:30:26Z","links":{"resolver":"https://pith.science/pith/5377NQD547C7SYTKAWIVTACPR5","bundle":"https://pith.science/pith/5377NQD547C7SYTKAWIVTACPR5/bundle.json","state":"https://pith.science/pith/5377NQD547C7SYTKAWIVTACPR5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5377NQD547C7SYTKAWIVTACPR5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5377NQD547C7SYTKAWIVTACPR5","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":"7289dce2e88c8aca593dd5ae8f968c296281a4c9b99df7033853201e997be23f","cross_cats_sorted":["math-ph","math.AP","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-06T22:27:38Z","title_canon_sha256":"b0351d80ddc27f6022b8dd5fc05fb5174abe718fbe041b0f85e46be7d84c9295"},"schema_version":"1.0","source":{"id":"1707.01984","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01984","created_at":"2026-05-18T00:08:23Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01984v3","created_at":"2026-05-18T00:08:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01984","created_at":"2026-05-18T00:08:23Z"},{"alias_kind":"pith_short_12","alias_value":"5377NQD547C7","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5377NQD547C7SYTK","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5377NQD5","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:3f8df221082cd9c30b14ef3d081195b27f12b01f110aa2f2e6694fa27719a42f","target":"graph","created_at":"2026-05-18T00:08:23Z","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 introduce generalized dynamical pruning on rooted binary trees with edge lengths. The pruning removes parts of a tree $T$, starting from the leaves, according to a pruning function defined on subtrees within $T$. The generalized pruning encompasses a number of discrete and continuous pruning operations, including the tree erasure and Horton pruning. The main result is invariance of a finite critical binary Galton-Watson tree with exponential edge lengths with respect to the generalized dynamical pruning for an arbitrary admissible pruning function. The second part of the paper examines the ","authors_text":"Ilya Zaliapin, Yevgeniy Kovchegov","cross_cats":["math-ph","math.AP","math.DS","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-06T22:27:38Z","title":"Dynamical pruning of rooted trees with applications to 1D ballistic annihilation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01984","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":"sha256:99c86cfc09cef36ecbb8f45d6f719b88fc9e772a663be293c58000c648a8a934","target":"record","created_at":"2026-05-18T00:08:23Z","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":"7289dce2e88c8aca593dd5ae8f968c296281a4c9b99df7033853201e997be23f","cross_cats_sorted":["math-ph","math.AP","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-06T22:27:38Z","title_canon_sha256":"b0351d80ddc27f6022b8dd5fc05fb5174abe718fbe041b0f85e46be7d84c9295"},"schema_version":"1.0","source":{"id":"1707.01984","kind":"arxiv","version":3}},"canonical_sha256":"eefff6c07de7c5f9626a059159804f8f620075e2c9a10038d9f6d6a2bf4859cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eefff6c07de7c5f9626a059159804f8f620075e2c9a10038d9f6d6a2bf4859cb","first_computed_at":"2026-05-18T00:08:23.616610Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:23.616610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s9P1DO+6W25xLsF+4rglncyoVIWRgSI+dX+8TIct5q3evAw9q5fbrCyJHZFAHnB8O8qQ+kc1c/GnoeImRhg/Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:23.617039Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.01984","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99c86cfc09cef36ecbb8f45d6f719b88fc9e772a663be293c58000c648a8a934","sha256:3f8df221082cd9c30b14ef3d081195b27f12b01f110aa2f2e6694fa27719a42f"],"state_sha256":"1035ef3a608f89ddc235c5f5fb552903eafbf721f37e3f8a0f02f4da38ec9515"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wyJIYPVOSM10XoPWja4Sko8fedGh2M/KYSu2yRb5GpKG2Fd8I01vxL8LMaR6b69W3HA/SmwUhhCffJzJujW/BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T06:30:26.572250Z","bundle_sha256":"ea0c3959aea11ef99c1e3fc50c29caab0c0972e09dd7ea15e4c032c2256ffe56"}}